# Thread: Dark Matter, Dark Energy and the Hyperbolic Gravitational Field

1. Black holes are singularities. This means that they must exist as point masses, according to general relativity. The gravitational field around a point mass must have a hyperbolic potential profile, not a parabolic one as assumed by Newton’s Law of Gravity. This is because the event horizon of a black-hole is not a true surface like that of a planet or a surface zone like that of a star. The only characteristic of a black-hole that makes any difference here is the point-mass at the Heisenberg uncertainty constrained center. Mordechai Milgrom's work (see below) proves that there is more to a black-hole than just its event horizon.

A hyperbola is characterized by asymptotes that define the extreme behavior of the curve far from the origin. Hyperbolic curves merely approach, but never reach the asymptotes. Proper parabolas, on the other hand, approach and reach their extreme values eventually. For instance, a proper parabola will actually pass through the origin, but the equivalent hyperbola never will.

The hyperbolic gravitational field profile (a 2D graph) around a black hole has significant consequences. These effects include a much slower fall-off of the gravitational potential as one proceeds to larger distances, r, from the origin. The mass of the supermassive black hole at the center of most spiral galaxies is a few million solar masses at most. But, the mass of the entire galaxy is several hundred billion solar masses. So, it would seem that the mass of the central black hole is insignificant relative to the galaxy as a whole. But, since the gravitational fields of the black hole and of the galaxy must be perfectly aligned and co-axial, the fields must superpose, reinforce and merge as one. So, the effective mass of the central black hole must be in the hundreds of billions of solar masses. The consequence of this is that the gravitational field experienced by any given star or group of stars near the periphery of a spiral galaxy must be declining as 1/r*, by the definition of a hyperbola, not as 1/r2, according to Newton’s Law. The unit vector, r, allows proper dimensional analysis. It is a constant, so the equation, say, F = GmM/ r*, is hyperbolic in nature. The symbol, r*, is the variable r (distance from the graphical origin or from the center of a galaxy) multiplied by the dimensioned value of the unit vector associated with the vector equivalent of r, (r1). This ensures that the "hyperbolic" Newtonian equation F = GmM/r* passes dimensional analysis. But, there are other fundamental justifications for its use. Normally we use the "parabolic" form F = GmM/r2. But not when super-massive black holes are involved.

This explains the MOND effect, the residual gravitational potential constant that was observed by Mordehai Milgrom in 1983 for stars near the peripheries of spiral galaxies. MOND stands for Modified Newtonian dynamics, a proposed revision of Newton’s Law. I call it the “MOND effect” to distinguish it from MOND itself because when the hyperbolic (proportional to 1/r*) gravitational field is considered, no modification of Newton’s Law is required. Instead, a footnote must be appended to acknowledge that a hyperbolic 1/r* field can exist around black holes.

Another consequence is that there is no need to hypothesized “Dark Matter”. The rotational distribution effects around galaxies and the behavior of galactic clusters and super-clusters is explained by the hyperbolic black hole gravitational field effect. The behavior of colliding galaxies having hyperbolic gravitational fields that are in the process of merging is also explained.

Since the hypothesis of the existence of a huge point mass called an “inflaton” is used to explain numerous characteristics of the cosmic microwave background radiation (CMB) and the expansion of the universe, it makes sense to consider that the universe was once immersed in a hyperbolic 1/r* gravitational field. The inflaton itself can be said to have existed before the Big Bang (BB). So, its hyperbolic gravitational field must have existed then too.

The question arises: What happened to the hyperbolic field after the BB? At the instant of the BB, the hyperbolic field must have begun to collapse or transition from a hyperbolic field to a parabolic Newtonian filed. This transition should still be occurring, the process requiring the entire lifetime of the universe to complete. The hyperbolic field is inherently more intense than the equivalent parabolic field, so the transition to the weaker field must be releasing potential energy. This energy will show up as kinetic energy in the form of the accelerating expansion rate of the universe.

So, the source of “Dark Energy” is gravitational, not due to a new type of field called "quintessence". It would give a positive cosmological constant, Lambda, in the Friedmann equations under the FLRW metric. These are relativistic treatments, but the hyperbolic 1/r* gravitational field equations are purely Newtonian. Nevertheless, no “quintessence” field is needed, just as no “Dark Matter” is needed to explain the MOND effect.

2.

3. Originally Posted by Gary Anthony Kent
Black holes are singularities. This means that they must exist as point masses, according to general relativity. The gravitational field around a point mass must have a hyperbolic potential profile, not a parabolic one as assumed by Newton’s Law of Gravity..
Hi Gary, long time no C, I'm glad you're back, hope you'll continue discussion on the shape of the universe, there was some noise there.

Now tell me, they say at center of earth gravity is 0, shouldn't it be the same everywhere, even in a BH?

4. Originally Posted by Gary Anthony Kent
Black holes are singularities. This means that they must exist as point masses, according to general relativity.

Actually, that is not quite correct, and although it is a commonly used analogy for what a black hole represents in popularisations, it doesn't tell the real story.

In general relativity, the singularity associated with a black hole is a singularity in space-time where time-like geodesics cannot be arbitrarily extended in the forward direction. The singularity associated with the Big-Bang is one where time-like geodesics cannot be extended in the backwards direction. There are no singular points in the space-time manifold, and therefore no point masses, as such, so the hyperbolic point seems moot here.

Or to put it another way, all the mass in a black hole does not have to exist as a point (if such a thing were possible) for a black hole to form. The black hole forms as a direct result of gravitational collapse, where mass falls inwards at such a rate that an event horizon forms once all the mass has collapsed to within the Schwarzschild radius of the object in question. As soon as there is a certain density within a certain region, as the mass collapses inwards, the event horizon emerges as the mass passes that point. We now have a black hole, without any "point masses", and time and space mean different things inside the event horizon.

The space-time inside the event horizon is not part of the universe outside the event horizon, any more.

Outside the event horizon, gravity points towards the centre of the black hole, as it does with all objects (aside from frame dragging issues due to rotation, of course), however dense or large they are. I fail to see how a black hole would act differently at a distance, gravitationally, to whatever formed it in the first place.

The question as to whether the mass in a black hole ends up compressed into a singular point, or not, is not actually within the domain of applicability of general relativity, as we are dealing here with events occurring at the quantum scale, so it is doubtful that general relativity would accurately describe events in those conditions - what we need for this is a theory of quantum gravity.

So the question that comes to my mind is, what causes the hyperbolic behaviour that deviates from the standard inverse-squared behaviour at a distance, when a star collapses and forms a black hole? To the outside universe, the gravitational collapse is still occurring (time stops for the outside universe at the event horizon), so even if the singularity is a "point mass", it hasn't formed yet, unless you are inside the event horizon. Or are you actually implying that all gravity is hyperbolic?

Originally Posted by Gary Anthony Kent
Since the hypothesis of the existence of a huge point mass called an “inflaton” is used to explain numerous characteristics of the cosmic microwave background radiation (CMB) and the expansion of the universe, it makes sense to consider that the universe was once immersed in a hyperbolic gravitational field. The inflaton itself can be said to have existed before the Big Bang (BB). So, its hyperbolic gravitational field must have existed then too.

Do you have a source for the "inflaton" hypothesis you describe as being a "huge point mass"? It sounds a lot like Guth's Inflation theory, which contains an inflaton field, but I don't remember seeing the inflaton field ever described as a "huge point mass", which seems to be a contradictory description.

How can a point be huge, and not be a volume?

I don't think the inflaton field can be said to have existed before the BB either, nor can it be described as hyperbolic where the universe is concerned, as inflationary physics treats the universe as being homogeneous and isotropic. There is nowhere different for it be hyperbolic in relation to.

5. Originally Posted by ray
Now tell me, they say at center of earth gravity is 0, shouldn't it be the same everywhere, even in a BH?
That's a good question!

It is true for spherical objects with uniform density, but black holes are a bit of an exception, as you might guess. Once all the mass of an object exists within the Schwarzschild radius of the object, all bets are off!

If time points at and ends at a singularity, then the gravity there would be undefined.

6. Newtonian universal gravity doesn't simply predict parabolas. It predicts conic sections. It's trajectory that determines the conic section used.Regardless, this thread is more pure fantasy.

7. [QUOTE=SpeedFreek;286381]
Originally Posted by ray
Now tell me, they say at center of earth gravity is 0, shouldn't it be the same everywhere, even in a BH?[/QUOTE
black holes are a bit of an 1)exception, as you might guess. Once all the mass of an object exists within the Schwarzschild radius of the object, all 3)bets are off!
If time points at and ends at a singularity, then the gravity there would be 2)undefined.
there you go again , 1) exceptions must be justified, 2)that's not science 3) this time it's not magic, Ladbrokes

8. You want me to go into an in depth examination of black holes in order to show how the gravitational force cannot be described as 0 at the singularity? There is no simpler way to do it, other than that, so you expect a full scientific exposition every time you ask a question? Or I can just go straight to the answer and give it to you.

There are various issues that need to be dealt with, in order to discuss this in depth. Words like "direction" have a different meaning, inside the event horizon. Once inside, as an analogy, it is as if the spatial and temporal dimensions have changed round for an in-falling observer - all directions lead to the singularity and the only thing you change via your own acceleration in any direction would be the time it takes for you to reach the singularity.

Depending on the mass of the black hole, matter will either be ripped apart by gravitational tidal forces, outside or inside the event horizon, but always before anything reaches the singularity.

Perhaps a good description would here would be, yet again, to put it like this:

For there to be a measure of gravitational force, there has to be somewhere else for the measurement to be relative to. Wherever you are in relation to the centre of something, gravity points you towards the centre. When you are at the centre, you feel zero gravitational force because the gravity of all the matter above you, in each direction, cancels out.

But at a singularity, there is no "above" you, in any direction. There is no direction that doesn't lead to the singularity, so once you reach the singularity, gravity is undefined. You have no space if you exist within a singular point.

If you want anything better than that, it will require a more formal presentation. This is why you get links to the relevant papers, rather than me having to translate the contents of those papers into a form small enough to fit into one post:

[astro-ph/9801252] Black Holes : A General Introduction

9. if a hat doesn't fit, I hope you don't change your head, but the hat.. if a theory breaks down at a certain point, you discard it, not reality

10. I don't know why I bother...

11. I suggest a good read will help clear up the apparent mysteries associated with singularity type behavour ray,sorry if i was ad hom previously..
.its just that when you really have a good grip on what are these apparent paradoxical attributes,then nothing makes better sense in a logical way...there is indeed a bigger picture...
I could personally recommend studying string theory,as described by Leonard Susskind regarding what the information paradox is all about...even hawking(not meant in a disrespectful way,as hawking is the other leading expert in singularities) was resigned to agree that susskinds' theory was more fully describing what seems to be going on... obviously mine is just an opinion

12. Originally Posted by ray
Originally Posted by Gary Anthony Kent
Black holes are singularities. This means that they must exist as point masses, according to general relativity. The gravitational field around a point mass must have a hyperbolic potential profile, not a parabolic one as assumed by Newton’s Law of Gravity..
Hi Gary, long time no C, I'm glad you're back, hope you'll continue discussion on the shape of the universe, there was some noise there.

Now tell me, they say at center of earth gravity is 0, shouldn't it be the same everywhere, even in a BH?
The trouble is, one can never actually reach the center of a black hole, not even theoretically. This is because, due to the intense gravitational field, time slows down nearer and nearer to zero when the center is approached so that "you cannot get there from here". Nobody knows what may be at the exact center of a black hole. It may be a wormhole leading to another part of the universe or to a different universe. If you figure out how to visit the center of a black hole without being torn to shreds and crushed at the same time, contact me (see my profile).

13. Originally Posted by SpeedFreek
Originally Posted by Gary Anthony Kent
Black holes are singularities. This means that they must exist as point masses, according to general relativity.

Actually, that is not quite correct, and although it is a commonly used analogy for what a black hole represents in popularisations, it doesn't tell the real story.

In general relativity, the singularity associated with a black hole is a singularity in space-time where time-like geodesics cannot be arbitrarily extended in the forward direction. The singularity associated with the Big-Bang is one where time-like geodesics cannot be extended in the backwards direction. There are no singular points in the space-time manifold, and therefore no point masses, as such, so the hyperbolic point seems moot here.

Or to put it another way, all the mass in a black hole does not have to exist as a point (if such a thing were possible) for a black hole to form. The black hole forms as a direct result of gravitational collapse, where mass falls inwards at such a rate that an event horizon forms once all the mass has collapsed to within the Schwarzschild radius of the object in question. As soon as there is a certain density within a certain region, as the mass collapses inwards, the event horizon emerges as the mass passes that point. We now have a black hole, without any "point masses", and time and space mean different things inside the event horizon.

The space-time inside the event horizon is not part of the universe outside the event horizon, any more.

Outside the event horizon, gravity points towards the centre of the black hole, as it does with all objects (aside from frame dragging issues due to rotation, of course), however dense or large they are. I fail to see how a black hole would act differently at a distance, gravitationally, to whatever formed it in the first place.

The question as to whether the mass in a black hole ends up compressed into a singular point, or not, is not actually within the domain of applicability of general relativity, as we are dealing here with events occurring at the quantum scale, so it is doubtful that general relativity would accurately describe events in those conditions - what we need for this is a theory of quantum gravity.

So the question that comes to my mind is, what causes the hyperbolic behaviour that deviates from the standard inverse-squared behaviour at a distance, when a star collapses and forms a black hole? To the outside universe, the gravitational collapse is still occurring (time stops for the outside universe at the event horizon), so even if the singularity is a "point mass", it hasn't formed yet, unless you are inside the event horizon. Or are you actually implying that all gravity is hyperbolic?

Originally Posted by Gary Anthony Kent
Since the hypothesis of the existence of a huge point mass called an “inflaton” is used to explain numerous characteristics of the cosmic microwave background radiation (CMB) and the expansion of the universe, it makes sense to consider that the universe was once immersed in a hyperbolic gravitational field. The inflaton itself can be said to have existed before the Big Bang (BB). So, its hyperbolic gravitational field must have existed then too.

Do you have a source for the "inflaton" hypothesis you describe as being a "huge point mass"? It sounds a lot like Guth's Inflation theory, which contains an inflaton field, but I don't remember seeing the inflaton field ever described as a "huge point mass", which seems to be a contradictory description.

How can a point be huge, and not be a volume?

I don't think the inflaton field can be said to have existed before the BB either, nor can it be described as hyperbolic where the universe is concerned, as inflationary physics treats the universe as being homogeneous and isotropic. There is nowhere different for it be hyperbolic in relation to.
Yes, I refer to Guth's Inflation hypothesis. I also refer to black holes as "huge" singularities only insofar as their masses must be huge.

From Wikipedia under "Schwartzchild Metric":

The case r = 0 is different, however. If one asks that the solution be valid for all r one runs into a true physical singularity, or gravitational singularity, at the origin. To see that this is a true singularity one must look at quantities that are independent of the choice of coordinates. One such important quantity is the Kretschmann invariant;

(which says) at r = 0 the curvature blows up (becomes infinite) indicating the presence of a singularity. At this point the metric, and space-time itself, is no longer well-defined. For a long time it was thought that such a solution was non-physical. However, a greater understanding of general relativity led to the realization that such singularities were a generic feature of the theory and not just an exotic special case. Such solutions are now believed to exist and are termed black holes.

14. Originally Posted by Gary Anthony Kent
The trouble is, one can never actually reach the center of a black hole,.... If you figure out how to visit the center of a black hole without being torn to shreds and crushed at the same time, contact me (see my profile).
that is not a valid argument, because nobody can reach or visited the center of earth or of an atom, and yet we have a coherent, plausible explanation.

15. Originally Posted by Gary Anthony Kent
The trouble is, one can never actually reach the center of a black hole, not even theoretically. This is because, due to the intense gravitational field, time slows down nearer and nearer to zero when the center is approached so that "you cannot get there from here". Nobody knows what may be at the exact center of a black hole. It may be a wormhole leading to another part of the universe or to a different universe. If you figure out how to visit the center of a black hole without being torn to shreds and crushed at the same time, contact me (see my profile).
Actually, it this is not a valid argument because it is completely incorrect. The proper time of an infaller never slows down, and the infaller reaches the singularity in a finite time. The coordinate time of the infaller, as seen by a distant observer, seems to stop at the event horizon (not the centre), but this is a coordinate effect.

You should read the Introduction to black holes I posted earlier in this thread. Section 2.2 covers the difference between proper time and coordinate time (referred to as "apparent" time in the paper).

16. Originally Posted by Gary Anthony Kent
Originally Posted by SpeedFreek
Originally Posted by Gary Anthony Kent
Black holes are singularities. This means that they must exist as point masses, according to general relativity.

Actually, that is not quite correct, and although it is a commonly used analogy for what a black hole represents in popularisations, it doesn't tell the real story.

In general relativity, the singularity associated with a black hole is a singularity in space-time where time-like geodesics cannot be arbitrarily extended in the forward direction. The singularity associated with the Big-Bang is one where time-like geodesics cannot be extended in the backwards direction. There are no singular points in the space-time manifold, and therefore no point masses, as such, so the hyperbolic point seems moot here.

Or to put it another way, all the mass in a black hole does not have to exist as a point (if such a thing were possible) for a black hole to form. The black hole forms as a direct result of gravitational collapse, where mass falls inwards at such a rate that an event horizon forms once all the mass has collapsed to within the Schwarzschild radius of the object in question. As soon as there is a certain density within a certain region, as the mass collapses inwards, the event horizon emerges as the mass passes that point. We now have a black hole, without any "point masses", and time and space mean different things inside the event horizon.

The space-time inside the event horizon is not part of the universe outside the event horizon, any more.

Outside the event horizon, gravity points towards the centre of the black hole, as it does with all objects (aside from frame dragging issues due to rotation, of course), however dense or large they are. I fail to see how a black hole would act differently at a distance, gravitationally, to whatever formed it in the first place.

The question as to whether the mass in a black hole ends up compressed into a singular point, or not, is not actually within the domain of applicability of general relativity, as we are dealing here with events occurring at the quantum scale, so it is doubtful that general relativity would accurately describe events in those conditions - what we need for this is a theory of quantum gravity.

So the question that comes to my mind is, what causes the hyperbolic behaviour that deviates from the standard inverse-squared behaviour at a distance, when a star collapses and forms a black hole? To the outside universe, the gravitational collapse is still occurring (time stops for the outside universe at the event horizon), so even if the singularity is a "point mass", it hasn't formed yet, unless you are inside the event horizon. Or are you actually implying that all gravity is hyperbolic?

Originally Posted by Gary Anthony Kent
Since the hypothesis of the existence of a huge point mass called an “inflaton” is used to explain numerous characteristics of the cosmic microwave background radiation (CMB) and the expansion of the universe, it makes sense to consider that the universe was once immersed in a hyperbolic gravitational field. The inflaton itself can be said to have existed before the Big Bang (BB). So, its hyperbolic gravitational field must have existed then too.

Do you have a source for the "inflaton" hypothesis you describe as being a "huge point mass"? It sounds a lot like Guth's Inflation theory, which contains an inflaton field, but I don't remember seeing the inflaton field ever described as a "huge point mass", which seems to be a contradictory description.

How can a point be huge, and not be a volume?

I don't think the inflaton field can be said to have existed before the BB either, nor can it be described as hyperbolic where the universe is concerned, as inflationary physics treats the universe as being homogeneous and isotropic. There is nowhere different for it be hyperbolic in relation to.
Yes, I refer to Guth's Inflation hypothesis. I also refer to black holes as "huge" singularities only insofar as their masses must be huge.

From Wikipedia under "Schwartzchild Metric":

The case r = 0 is different, however. If one asks that the solution be valid for all r one runs into a true physical singularity, or gravitational singularity, at the origin. To see that this is a true singularity one must look at quantities that are independent of the choice of coordinates. One such important quantity is the Kretschmann invariant;

(which says) at r = 0 the curvature blows up (becomes infinite) indicating the presence of a singularity. At this point the metric, and space-time itself, is no longer well-defined. For a long time it was thought that such a solution was non-physical. However, a greater understanding of general relativity led to the realization that such singularities were a generic feature of the theory and not just an exotic special case. Such solutions are now believed to exist and are termed black holes.
The wiki article is correct in what it says, but how does any of that support what you said about "point masses" and hyperbolic gravity? (clue: it does not)

17. .......................................

18. I simply make the observation that the so-called MOND effect itself can better be explained by the simple expedient of introducing the hyperbolic black hole (HBH) galactic gravitational field. MOND doesn't explain anything. As presented by Milgrom, it is an unnecessary complication.

Extrapolated to the entire universe, the HBH field effect serves as a mechanism whereby a continuing transition from a hyperbolic field to a parabolic gravitational field can provide energy to cause accelerated expansion of the universe. It is a mechanism whereby a positive cosmological constant can be achieved without any fuss.

19. From Wikipedia, the Schwartzchild Metric:

"The case r = 0 is different, however. If one asks that the solution be valid for all r one runs into a true physical singularity, or gravitational singularity, at the origin. To see that this is a true singularity one must look at quantities that are independent of the choice of coordinates. One such important quantity is the Kretschmann invariant (which says) at r = 0 the curvature blows up (becomes infinite) indicating the presence of a singularity. At this point the metric, and space-time itself, is no longer well-defined. For a long time it was thought that such a solution was non-physical. However, a greater understanding of general relativity led to the realization that such singularities were a generic feature of the theory and not just an exotic special case. Such solutions are now believed to exist and are termed black holes."

Yes, there are alternate definitions of black holes. But, black holes not containing real and true gravitational singularities is not a part of any of them.

Not only were there acoustic oscillations, but quantum statistical variations during the "inflation" era that helped cause coalescence of matter into galaxies and galactic clusters. But, which came first, black holes or galaxies? As soon as galaxies began to form, so did black holes and their exceptional gravitational fields had their effect right from the beginning.

So, no dark matter is required to explain these and other effects that have been blamed on dark matter.

Yes, there is no conflict here with the idea of a positive cosmological constant, but no "quintessence field" is required to explain it. Instead, the black hole hyperbolic gravitational field effect serves as a source for the potential energy that is said to be powering accelerating expansion of the universe.

I should think that cosmologists would heartily support a simpler explanation that does not require another field or force like quintessence. This ad hoc hypothesis greatly complicates the standard model and raises more questions than it settles.

20. Originally Posted by SpeedFreek
Originally Posted by Gary Anthony Kent
The trouble is, one can never actually reach the center of a black hole, not even theoretically. This is because, due to the intense gravitational field, time slows down nearer and nearer to zero when the center is approached so that "you cannot get there from here". Nobody knows what may be at the exact center of a black hole. It may be a wormhole leading to another part of the universe or to a different universe. If you figure out how to visit the center of a black hole without being torn to shreds and crushed at the same time, contact me (see my profile).
Actually, it this is not a valid argument because it is completely incorrect. The proper time of an infaller never slows down, and the infaller reaches the singularity in a finite time. The coordinate time of the infaller, as seen by a distant observer, seems to stop at the event horizon (not the centre), but this is a coordinate effect.

You should read the Introduction to black holes I posted earlier in this thread. Section 2.2 covers the difference between proper time and coordinate time (referred to as "apparent" time in the paper).

From Wikipedia, the Schwartzchild Metric:

"The case r = 0 is different, however. If one asks that the solution be valid for all r one runs into a true physical singularity, or gravitational singularity, at the origin. To see that this is a true singularity one must look at quantities that are independent of the choice of coordinates. One such important quantity is the Kretschmann invariant (which says) at r = 0 the curvature blows up (becomes infinite) indicating the presence of a singularity. At this point the metric, and space-time itself, is no longer well-defined. For a long time it was thought that such a solution was non-physical. However, a greater understanding of general relativity led to the realization that such singularities were a generic feature of the theory and not just an exotic special case. Such solutions are now believed to exist and are termed black holes."

The main point of my post is that "quintessence" is unnecessary to explain the accelerating expansion rate of the universe. We should not be caught in the rabbit runs of infinite detail. I would rather that we focus on main points. If quintessence is unnecessary, then no revision of the standard model of particle physics is needed. No jiggering of theory is required to admit quintessence. I should think that physicists would be happy about this.

21. Originally Posted by Gary Anthony Kent
You can repeat the wiki definition of the singularity at the origin (r=0) as much as you like, but you still need to point out how it supports what you are saying about hyperbolic gravity, dark matter and dark energy (or quintessence). So far, all we have is a statement that the gravity of a black hole should be hyperbolic, but nothing to back it up.

22. Originally Posted by SpeedFreek
Originally Posted by Gary Anthony Kent
You can repeat the wiki definition of the singularity at the origin (r=0) as much as you like, but you still need to point out how it supports what you are saying about hyperbolic gravity, dark matter and dark energy (or quintessence). So far, all we have is a statement that the gravity of a black hole should be hyperbolic, but nothing to back it up.
I don't know why I bother either.

The existence of the "MOND effect" is a necessary and sufficient logical support.

Note that I call it the "MOND effect". I do not endorse MOND. But, Milgrom's data are good. No Dark Matter is needed, however, not even as an alternative to MOND.

23. Originally Posted by SpeedFreek
Originally Posted by Gary Anthony Kent
Originally Posted by SpeedFreek
Originally Posted by Gary Anthony Kent
Black holes are singularities. This means that they must exist as point masses, according to general relativity.

Actually, that is not quite correct, and although it is a commonly used analogy for what a black hole represents in popularisations, it doesn't tell the real story.

In general relativity, the singularity associated with a black hole is a singularity in space-time where time-like geodesics cannot be arbitrarily extended in the forward direction. The singularity associated with the Big-Bang is one where time-like geodesics cannot be extended in the backwards direction. There are no singular points in the space-time manifold, and therefore no point masses, as such, so the hyperbolic point seems moot here.

Or to put it another way, all the mass in a black hole does not have to exist as a point (if such a thing were possible) for a black hole to form. The black hole forms as a direct result of gravitational collapse, where mass falls inwards at such a rate that an event horizon forms once all the mass has collapsed to within the Schwarzschild radius of the object in question. As soon as there is a certain density within a certain region, as the mass collapses inwards, the event horizon emerges as the mass passes that point. We now have a black hole, without any "point masses", and time and space mean different things inside the event horizon.

The space-time inside the event horizon is not part of the universe outside the event horizon, any more.

Outside the event horizon, gravity points towards the centre of the black hole, as it does with all objects (aside from frame dragging issues due to rotation, of course), however dense or large they are. I fail to see how a black hole would act differently at a distance, gravitationally, to whatever formed it in the first place.

The question as to whether the mass in a black hole ends up compressed into a singular point, or not, is not actually within the domain of applicability of general relativity, as we are dealing here with events occurring at the quantum scale, so it is doubtful that general relativity would accurately describe events in those conditions - what we need for this is a theory of quantum gravity.

So the question that comes to my mind is, what causes the hyperbolic behaviour that deviates from the standard inverse-squared behaviour at a distance, when a star collapses and forms a black hole? To the outside universe, the gravitational collapse is still occurring (time stops for the outside universe at the event horizon), so even if the singularity is a "point mass", it hasn't formed yet, unless you are inside the event horizon. Or are you actually implying that all gravity is hyperbolic?

Originally Posted by Gary Anthony Kent
Since the hypothesis of the existence of a huge point mass called an “inflaton” is used to explain numerous characteristics of the cosmic microwave background radiation (CMB) and the expansion of the universe, it makes sense to consider that the universe was once immersed in a hyperbolic gravitational field. The inflaton itself can be said to have existed before the Big Bang (BB). So, its hyperbolic gravitational field must have existed then too.

Do you have a source for the "inflaton" hypothesis you describe as being a "huge point mass"? It sounds a lot like Guth's Inflation theory, which contains an inflaton field, but I don't remember seeing the inflaton field ever described as a "huge point mass", which seems to be a contradictory description.

How can a point be huge, and not be a volume?

I don't think the inflaton field can be said to have existed before the BB either, nor can it be described as hyperbolic where the universe is concerned, as inflationary physics treats the universe as being homogeneous and isotropic. There is nowhere different for it be hyperbolic in relation to.
Yes, I refer to Guth's Inflation hypothesis. I also refer to black holes as "huge" singularities only insofar as their masses must be huge.

From Wikipedia under "Schwartzchild Metric":

The case r = 0 is different, however. If one asks that the solution be valid for all r one runs into a true physical singularity, or gravitational singularity, at the origin. To see that this is a true singularity one must look at quantities that are independent of the choice of coordinates. One such important quantity is the Kretschmann invariant;

(which says) at r = 0 the curvature blows up (becomes infinite) indicating the presence of a singularity. At this point the metric, and space-time itself, is no longer well-defined. For a long time it was thought that such a solution was non-physical. However, a greater understanding of general relativity led to the realization that such singularities were a generic feature of the theory and not just an exotic special case. Such solutions are now believed to exist and are termed black holes.
The wiki article is correct in what it says, but how does any of that support what you said about "point masses" and hyperbolic gravity? (clue: it does not)
Presumably, when the universe formed from Alan Guth's inflaton, its hyperbolic gravitational field began to collapse into a parabolic one (see post of Sept. 19, 2011). That collapse continues to this day. But, the process is almost done. There cannot be an infinite amount of gravitational energy sequestered in the hyperbolic field that would be available to fuel acceleration of the expansion rate via such a transformation. That is, transition to a lower energy parabolic field must provide a distinctly limited supply of extra impetus. Surely, after 13.72 billion years, the spring has almost run down by now.

If the expansion rate is called h, and its present value is called P, then h = P at any given time, including the present. The simplest equation for the expansion rate’s effect on P would be an exponential decay expression, P = h0e-rt, where h0 is an initial value for the expansion rate, h, r is the rate of increase in this expansion and t is time.

We can get an estimate of a value for h0 from Alan Guth’s formulation of the theory of simple inflation. The present values of both the expansion rate, P1, and acceleration rate, r, are observable. We can set t = 1, for the present value of t. So, we can summarize all relevant observations with this simple equation or the associated exponential expansion equation,
R = R0ert, where R is the putative “radius” or scale factor of the universe.

The current value (at t = 1) of the expansion rate is H0, the Hubble “constant”, so P1 = H0.

Exponential decay equations exhibit what is called a “dormancy” period or final plateau region. The hyperbolic curve levels off near zero and continues to subside gently almost linearly for an indefinite time. The current state of the universe may be consistent with this dormant period. The conclusion here is that acceleration may continue for a long time while slowly decreasing nearer to zero. In other words, even with acceleration of the expansion rate, there does not necessarily have to be a “Big Rip” wherein the fabric of the cosmos is irreparably torn apart as expansion proceeds beyond a certain point.

The point made about point masses and singularities engendering a hyperbolic gravitational field is a mathematical necessity. Consider what a point mass as a singularity actually means. If it does not mean that they generate a hyperbolic gravitational field, then the words point mass and singularity are meaningless. Karl Schwartzchild would not agree with this negation of his analysis of general relativity.

24. Originally Posted by brane wave
I suggest a good read will help clear up the apparent mysteries associated with singularity type behavour ray,sorry if i was ad hom previously..
.its just that when you really have a good grip on what are these apparent paradoxical attributes,then nothing makes better sense in a logical way...there is indeed a bigger picture...
I could personally recommend studying string theory,as described by Leonard Susskind regarding what the information paradox is all about...even hawking(not meant in a disrespectful way,as hawking is the other leading expert in singularities) was resigned to agree that susskinds' theory was more fully describing what seems to be going on... obviously mine is just an opinion
String theory has not produced one single experimentally verified unique insight. It does not hold a candle to general relativity, which has been experimentally validated in many ways. And, Hawking has tetracted his opinion that information is lost when matter falls into a black hole. He now says, and many analysts agree, that information is stored on the "surface" or event horizon of black holes as entropy and can be "recovered" via "Hawking radiation".

The only way to settle the debate about the hyperbolic black-hole gravitational field effect is experimentally. Milgrom's data are only a start.
Failure to find any trace of Dark Matter would help. Failure to pinpoint the "MOND effect" on smaller scales than galaxies would also help. But, this would only be supporting evidence. We can pick each others' arguments apart by focussing on trivia forever and ever. We can misread one anothers' posts too, or overlook their implications. The only way out is experimentation (or observation).

25. Originally Posted by Gary Anthony Kent
I don't know why I bother either.

The existence of the "MOND effect" is a necessary and sufficient logical support.

Note that I call it the "MOND effect". I do not endorse MOND. But, Milgrom's data are good. No Dark Matter is needed, however, not even as an alternative to MOND.
Please. Pick a galaxy where people measure the amount of dark matter and show us how to predict the rotation curve for that galaxy.

26. Originally Posted by PhysBang
Newtonian universal gravity doesn't simply predict parabolas. It predicts conic sections. It's trajectory that determines the conic section used.Regardless, this thread is more pure fantasy.
So what?

Fantasy has a disturbing tendency to become scientific fact.

27. Originally Posted by PhysBang
Originally Posted by Gary Anthony Kent
I don't know why I bother either.

The existence of the "MOND effect" is a necessary and sufficient logical support.

Note that I call it the "MOND effect". I do not endorse MOND. But, Milgrom's data are good. No Dark Matter is needed, however, not even as an alternative to MOND.
Please. Pick a galaxy where people measure the amount of dark matter and show us how to predict the rotation curve for that galaxy.
Predictions of actual galactic rotation velocity distributions abound. I won't re-invent the wheel. The "amount" of Dark Matter has been putatively measured using Milgrom's data itself. Its presumed existence is why the standard model is often called the L/CDM model, for Lamda/Cold Dark Matter under the Friedmann equations and the FLRW metric.

28. Originally Posted by Gary Anthony Kent
Predictions of actual galactic rotation velocity distributions abound. I won't re-invent the wheel. The "amount" of Dark Matter has been putatively measured using Milgrom's data itself. Its presumed existence is why the standard model is often called the L/CDM model, for Lamda/Cold Dark Matter under the Friedmann equations and the FLRW metric.
This response is so wrong, I don't know where to begin.

First of all, you are attempting to reinvent the wheel. You want to do the calculations of gravity using, "a hyperbolic potential profile, not a parabolic one as assumed by Newton’s Law of Gravity." Presumably, this means using different equations that those currently used to predict galactic rotation curves. If this is the case, then let's see your calculations. If it's not the case, then it seems that your proposal has absolutely no content.

Second, the consensus model of cosmology is called an LCDM model because of the dark matter found in cosmological tests, not in tests of the dynamics of individual galaxies. But this is irrelevant to the basic claim that there should be some new way of calculating the gravitation of black holes.

So, we return to the fundamental question: what is the real difference that you are proposing and can you use it to actually do physics?

29. If you won't give me any credit, why should I not refrain reciprocally? Milgrom was the first to furnish evidence of Dark Matter, which is used to explain away Milgrom's call for a revision of Newton's Law. Milgrom's analysis provides sufficient grounds for support of cosmological tests of Dark Matter such as gravitational lensing and the Sunyaev-Zeldovich effect. My analysis says merely that Dark Matter, as such, is unnecessary. The hyperbolic field is fully capable of accounting for these and other phenomena. This implies that no WIMP (weakly interacting massive particle) will ever be found. It may be a waste of funds to search for it.

The use of Milgrom's MOND data is discussed in the Wikipedia article on Dark Matter.

The Bullet Cluster phenomenon can be explained by postulating the existence of dark black holes in both clusters that cause displacement of the center of masses by the necessary offsets. I like Dark Black Holes better than Dark Matter. Perhaps they are basically the same. The WIMP must be very massive indeed, say 10^6 sols or more. Thus, no supercollider will ever duplicate the effect, then.

30. Originally Posted by SpeedFreek
Originally Posted by Gary Anthony Kent
The trouble is, one can never actually reach the center of a black hole, not even theoretically. This is because, due to the intense gravitational field, time slows down nearer and nearer to zero when the center is approached so that "you cannot get there from here". Nobody knows what may be at the exact center of a black hole. It may be a wormhole leading to another part of the universe or to a different universe. If you figure out how to visit the center of a black hole without being torn to shreds and crushed at the same time, contact me (see my profile).
Actually, it this is not a valid argument because it is completely incorrect. The proper time of an infaller never slows down, and the infaller reaches the singularity in a finite time. The coordinate time of the infaller, as seen by a distant observer, seems to stop at the event horizon (not the centre), but this is a coordinate effect.

You should read the Introduction to black holes I posted earlier in this thread. Section 2.2 covers the difference between proper time and coordinate time (referred to as "apparent" time in the paper).
We must speak of the perspective from our point of view bcause we will never voluntarilly plunge ourselves into a black hole to find out what it may look like from the inside. We couldn't transmit our observations back to Earth anyway. Even Gedanken experiments have limits.

31. Originally Posted by SpeedFreek
Originally Posted by Gary Anthony Kent
You can repeat the wiki definition of the singularity at the origin (r=0) as much as you like, but you still need to point out how it supports what you are saying about hyperbolic gravity, dark matter and dark energy (or quintessence). So far, all we have is a statement that the gravity of a black hole should be hyperbolic, but nothing to back it up.

Only Me makes some good points to which I must respond:

 “ Originally Posted by OnlyMe in scienceforums.net 26/11/11 1) The infinitely deep gravitational wells and thus infinite gravitational potential of such is not consistent with experience. Infinite remains infinite despite the method of reduction. It is more likely that in practice a black hole does have volume and is not a point mass singularity. 2) We have no empirical evidence that the gravitational potential of a BH ever exceeds that requiring an escape velocity equivalent to . 3) There are many things described mathematically that we do not find in experience, observation and experiment. 4) By framing your argument based on the theoretical point singularity, you introduce the potential for, not only and infinite mass density, but also an associated infinite mass. Which could theoretically support the underlying conclusions. 5) It could be argued just as successfully that since GR describes space as dynamically interacting with matter/mass, and the Lense-Thirring or frame-dragging effect can be considered confirmed, that over time and regular orbital motions of the matter contained within a galactic system, the very weak interaction between matter and space responsible for the frame-dragging effect has a cumulative effect and that in mature galactic systems the involved space must be considered to be essentially inertially involved. 6) In such a circumstance, from within such a system the inertial aspect of the involved space would be unobservable, while from any frame of reference external to the galactic system it would be observed as a component of the orbital velocities of the involved galactic matter. This too could be argued to be not only consistent with GR but also with a view of Newtonian dynamics, where space is a dynamic component of the whole system. GR requires that space be dynamic and the Lense-Thirring or frame-dragging effect demonstrates that the dynamic nature of space cannot be limited to a cuvature we experience as gravitation. 7) The observed anomalies in the orbital velocities involving galactic rotation, are theirselves a problem of dynamics. A dynamic interaction from which the dynamic nature that GR bestows on space cannot be excluded from consideration. 8) No matter what trail we follow in an attempt to explain the involved anomolous observations, the inclusion of dark matter, MOND or viewing the whole as an inertial system composed of both matter and space, we are left with the same fundamental questions... What is inertia and gravitation and how are they related or connected? Personnally I believe the answer will lie in a hybrid of GR and QM. ”

OM: Thanks again for taking the time to compose your reply. My responses:

1) At very least, the necessary experience is Milgrom’s raw observations. What other relevant hard experience do we have concerning purported actual black holes? The galactic rotation anomaly must be explained. Milgrom wants to modify Newtonian dynamics in a way that would vastly complicate general relativity. I want to introduce the simple expedient concept of the hyperbolic black-hole gravitational field effect, which preserves and even enhances GR. Which of us has the more extreme proposal?

Infinite remains infinite despite the method of reduction. This means that infinities cannot be explained away (the ultimate reduction). The existence of infinities in the Math surely has meaning. Schwartzchild thought so. He did not attempt to explain his infinities away.

Okay, there could be limits on the idea of infinity in this case. Perhaps there are quantum mechanical constraints such as the fact that pinpointing the center of a black-hole would violate the Heisenberg Uncertainty Principle. But, if a black hole compresses to a diameter as small as a Planck distance, it would serve the same purpose as an infinitely dense point mass. That is, there would be no way to tell that a black-hole was not infinitely dense. Milgrom’s observations indicate that it really does behave this way. Whether it may actually be so is a theoretical point that Schwartzchild has already considered.

I know that infinites are anathema to mathematicians. Their squeemishness is misplaced in cosmology, however. What if it happens that it is actually more likely that a BH is a real point mass, as close as we can tell by QM, having as near to an infinite density that may be required to provide the proper effect (the real meaning of “infinite”).

2) Actually, this is irrelevant. We are speaking of the geometry of BHs and the influence this geometry must have on the structure of spacetime in the vicinity. The consequences are to be determined by observation and experiment. If the escape velocity does not actually exceed c nearer to the center of a BH, then there is no such thing as an event horizon anyway. Karl Schwartzchild would object. If the escape velocity may be exceeded only by a smidgen determined by the Heisenberg Principle, why not by something rather more than just a smidgen? We need only to suppose that the effective radius of a BH is small enough to produce the required effect, which we may then consider to approach that needed to give effectively infinite density. “Effectively” is the keyword.

3) The nausea experienced by some professional mathematicians upon contemplation of infinity is not matched by the feelings of some others who revel in the concept. In fact, there is a whole branch of mathematics devoted to it. I do not believe that professionals would devote their whole careers to studies that do not have even theoretical practical consequences. Math is beautiful, but is no “10”. And, it is a whore.

The mathematics of infinities engendered by the Schwartzchild analysis of GR serve as a flag signaling that there is something going on here. What we find in experience now does not equate to what may be found in the future. And, Milgrom’s observations are still extant. No revision of Newton’s Law of Gravity is needed. No Dark Matter is needed either (Dark Matter is based on Milgrom). Just a liberal tweak upon the concept of what it really means to be a black hole is all that is required. Sometimes liberalism makes sense.

4) Speaking of infinite mass, one would have to refer to the whole universe, at minimum. What if BHs are wormholes leading to this very same universe, but from a different perspective? Might it not then have an effectively infinite mass? But this is all an unnecessary complication. The potential need not be realized.

5) Okay. Now we have another possible alternative to Dark Matter.

6) Well, of course. Do we not always observe external galaxies from afar? It seems far fetched that we should ever observe the Milky Way from beyond. So, your idea means that it should be futile to try to detect the effect in our own galaxy. But, is not GR all about the curvature of spacetime and the dynamic effects that we can expect from such a curvature. Remember, the vector and tensor math of GR is derived from techniques used in hydrodynamics. The dynamic nature of fluids has a “frame dragging” equivalent. In other words, you are saying that GR is dynamic, not static. Even Newtonian “dynamics” is really static in nature because it cannot treat transitions between states which are time dependent. Time dependent variations between fluid states is often referred to as “turbulence”. Is there “turbulence” in the behavior of spacetime?

7) You amplify your comment that frame dragging style wrinkles on the face of GR could explain MOND and explain away Dark Matter. What if BOTH these wrinkles and the giant scar of the hyperbolic field effect should apply?

8) Wonderful. Fundamental questions are what science is all about. But, the anomalies do indeed need to be explained.

Good luck finding a valid hybrid of GR and Quantum. Instead of M Theory, maybe we can call it OM Theory.

Thanks for taking the time to read this. Further response along these lines would be appreciated.

27/11/11

32. Originally Posted by Gary Anthony Kent
If you won't give me any credit, why should I not refrain reciprocally?
Why do you need any credit? You are making scientific claims, you should produce scientific evidence. So far, all you have is words without any results.
Milgrom was the first to furnish evidence of Dark Matter, which is used to explain away Milgrom's call for a revision of Newton's Law. Milgrom's analysis provides sufficient grounds for support of cosmological tests of Dark Matter such as gravitational lensing and the Sunyaev-Zeldovich effect.
Not really. What is really relevant here is that no galactic rotation tests provide any bearing on the CMB anisotropy tests or the SDSS or 2dF surveys that use large-scale structure to measure the mass density of the universe.

This is what every cosmology textbook lays out. If you can show differently, then show it, don't merely claim it.
My analysis says merely that Dark Matter, as such, is unnecessary. The hyperbolic field is fully capable of accounting for these and other phenomena. This implies that no WIMP (weakly interacting massive particle) will ever be found. It may be a waste of funds to search for it.
You have shown us no analysis. Again, if you have some analysis, then show us with any galaxy that you want to chose.

I'm not trying to be insulting, I'm just trying to hold you to the reasonable standards of the field. There is a mountain of data for you to choose from to do some actual analysis, just do it.

33. Originally Posted by PhysBang
Originally Posted by Gary Anthony Kent
If you won't give me any credit, why should I not refrain reciprocally?
Why do you need any credit? You are making scientific claims, you should produce scientific evidence. So far, all you have is words without any results.
Milgrom was the first to furnish evidence of Dark Matter, which is used to explain away Milgrom's call for a revision of Newton's Law. Milgrom's analysis provides sufficient grounds for support of cosmological tests of Dark Matter such as gravitational lensing and the Sunyaev-Zeldovich effect.
Not really. What is really relevant here is that no galactic rotation tests provide any bearing on the CMB anisotropy tests or the SDSS or 2dF surveys that use large-scale structure to measure the mass density of the universe.

This is what every cosmology textbook lays out. If you can show differently, then show it, don't merely claim it.
My analysis says merely that Dark Matter, as such, is unnecessary. The hyperbolic field is fully capable of accounting for these and other phenomena. This implies that no WIMP (weakly interacting massive particle) will ever be found. It may be a waste of funds to search for it.
You have shown us no analysis. Again, if you have some analysis, then show us with any galaxy that you want to chose.

I'm not trying to be insulting, I'm just trying to hold you to the reasonable standards of the field. There is a mountain of data for you to choose from to do some actual analysis, just do it.
I cannot repeat often enough that Milgrom's raw data are one of the scientific tests that you seek. And, mathematical certitude requires no further proof. The hyperbolic field follows logically from geometric first principles. If GR treats black holes as singularities (point particles), not merely as entities having an event horizon and thus a radius, it would produce the hyperbolic 1/r dependence of gravity versus distance. Unfortunately, human language logic is all we have here right now. For GR to treat black holes as point particles it would imply that they should be treated statistically. But, such a treatment would be called quantum mechanics. We do not yet have a proven valid merger between GR and quantum. Still, if GR is still to be used, a super simple single item "line" element tensor consistent with a point particle, with other adjustments that were made reliably so that the related super simple vector matrices "diagonalize" properly and their determinants are valid, the 1/r relationship would just pop out. But, this would not be any more compelling or surprising than a textual display of simple logic. Both mathematics and language literal logic share one thing: their conclusions are syllogistically inevitable. A GR treatment of my thesis is on my agenda.

That galactic rotation tests do not address the problem is exactly my point! Only the hyperbolic gravity field will do so. MOND is invalid. Dark Matter is superfluous. But Milgrom's data are used to support Dark Matter (see Wikipedia). The hyperbolic field will answer for all the phenomena that have been observed, including gravitational lensing, the Sunyaev-Zeldovich effects and Bullet Cluster type anomalies (if it is supposed that Bullet style colliding clusters may contain appropriately offset distributions of dark black-holes).

I make logical arguments for what I report, not mere claims. And, I report only what theory and the facts suggest. But, cosmologists choose to overlook this information. I think it is because it is not Weird Strange Science. It is actually "old hat". No research funding here. It costs hundreds of thousands of dollars per year to support just a few graduate students by a single university faculty member. Cosmologists go to where the money is. This is but one of the things that is wrong with our system.

It is too easy to focus on irrelevant details and downright trivia in an attempt to demonstrate a high I.Q. If such a demonstration is desired, it would be more effective to make an idea work, to fix it. These discussions resemble demolition derbies. Everyone winds up driving a complete wreck. There are no winners.

34. OK, now we have no choice but to believe that you have absolutely no idea what you are talking about. If you can't actually use your talk of the "hyperbolic field" to calculate the trajectory of any particles whatsoever, then you really aren't doing physics.

Perhaps this is a fine piece of poetry, but it it would be a lie to call it science. And there is no hyperbole there.

35. Originally Posted by PhysBang
OK, now we have no choice but to believe that you have absolutely no idea what you are talking about. If you can't actually use your talk of the "hyperbolic field" to calculate the trajectory of any particles whatsoever, then you really aren't doing physics.

Perhaps this is a fine piece of poetry, but it it would be a lie to call it science. And there is no hyperbole there.
"Hyperbolic" gravity field refers to such summary representations as F = GmM/r* versus parabolic fields simply summarized by F = GmM/r2. As formulated, this has r* being r multiplied by the dimensioned numerical value of the unit vector of r, (r). The hyperbolic (proportional to 1/r*) gravitational force equation is purely Newtonian. Dimensional analysis works nicely. The trajectories of any particles that we care about are ellipses and circles for both. Hyperbolic trajectories occur, but such particles are unbound and soon escape the system.

Should I use absolute values of the unit vector? Maybe. A scalar multiplied by a vector is another vector and this is not meant to be a vector equation but rather a simple summarization or succinct representation, symbol or metaphor for a gravitational field.

I got some feedback about my reference to "hyperbolic" gravity fields from another source. So, in many cases, I clarified my references to hyperbolic (proportional to 1/r*) fields. I must still go back to edit certain posts in some other forums.

36. Read the books Inflation by Alan Guth and The Fabric of the Cosmos by Brian Greene.

The theory of inflation postulates that there was something before the Big Bang. It is the "inflaton" particle which sprang into existence at a high energy by quantum mechanical fluctuation. Along with the inflaton, there must have been a gravitational field. This field must have been one whereby F = |GmM/rr|, having a hyperbolic gravitational field profile. Normally, a Newtonian entity would have a parabolic (F = GmM/r^2) gravitational field profile. But the inflaton is the mother of all black-holes, or MOAB. As a black-hole, the inflaton MOAB must have had a hyperbolic (proportional to 1/|rr|) gravitational field because it is a point mass having only a center but zero radius. Zero within the bounds of the Heisenberg uncertainty principle, that is. The symbol r is the unit vector associated with r, the radial distance to the center in graphs like the field profile. This unit vector makes dimensional analysis work nicely. It is a constant, so the related equation for F is the equation for a hyperbola.

This has consequences because when the inflaton particle suddenly began to decay into the matter and energy we see today, the hyperbolic field began to decay as well. It began to transform into a parabolic (proportional to 1/r^2) gravity field because it was no longer a point-particle having zero radius. The profile of a hyperbolic gravitational field implies inherently higher energy than the equivalent parabolic field profile. So, as the hyperbolic field transitioned to a parabolic one, it released (and continues to release) its potential energy. This potential energy fueled and continues to fuel acceleration of the expansion rate of the universe (Hubble expansion). This acceleration effect is sometimes referred to as being due to Dark Energy. It is often suggested that Dark Energy stems from a fundamental new force, to be called "quintessence", but it could really be due to a gravitational effect as described here. A gravitational effect is called "Lamda", for Einstein's cosmological constant that he added to his general theory of relativity. Lamda has a positive value because decay of the hyperbolic (1/|rr|) field releases energy into the observable universe.

Look up the FLRW metric and the Friedmann equations as well as the Big Bang and Guth's inflation on the Internet. Wikipedia is a good place to start.

37. I completely believe this and offer perhaps my explanation. The dimension of time and space as we know it will end when this universe ends. And in the next universe we have to figure out together how to progress to the next one. Energy is constantly evolving and through logic the energy keeps moving through dimensions. When gravity is zero. Time as we know it does not exist. Time is simply a logic perception of the brain. Energy can move as fast as it wills itseIf. Traveling faster than everything logical will allow for the travel of time and space. Think about this equation. T=mc^2. Anyone with logic can understand that

38. Originally Posted by Gary Anthony Kent
Look up the FLRW metric and the Friedmann equations as well as the Big Bang and Guth's inflation on the Internet. Wikipedia is a good place to start.
But it is a horrible place to stop. I studied the FLRW metric in graduate school, I know what scientific evidence is used to support the inclusion of dark matter in cosmology and what isn't because I have read relevant scientific papers.

So far, all I have seen from you is little more than cutting and pasting and references to popular science sources.

Again, I ask you to actually show us how you propose to predict the rotation curve of any galaxy of your choice using your hyperbolic method. If you cannot do this, then you really do not have a theory.

39. Originally Posted by PhysBang
Originally Posted by Gary Anthony Kent
Look up the FLRW metric and the Friedmann equations as well as the Big Bang and Guth's inflation on the Internet. Wikipedia is a good place to start.
But it is a horrible place to stop. I studied the FLRW metric in graduate school, I know what scientific evidence is used to support the inclusion of dark matter in cosmology and what isn't because I have read relevant scientific papers.

So far, all I have seen from you is little more than cutting and pasting and references to popular science sources.

Again, I ask you to actually show us how you propose to predict the rotation curve of any galaxy of your choice using your hyperbolic method. If you cannot do this, then you really do not have a theory.
This is what you mean eh? Why didn't you say so?

I would formulate a nonlinear homogeneous differential equation(s) according to the the limits and conditions that are implied in my post. Then, I would solve it or them to produce an equation(s) that can be plotted or graphed like the ones at my website. I would probably not need to use Mathematica. But, I would consult papers that address this problem to be more certain that I am on the right track. These papers do produce predictions, but they are all flawed, some in major ways.

I could also plug some real numbers into the equations that I already have. I like TK Solver Plus for this because Mathematica is way too expensive for me.

The FLRW metric under the Cosmological Principle and the Friedmann equations come under some serious criticism (r.e. George Ellis). And, when speaking of conditions of extremely high gravitational fields and very short or long distances, they may break down by one mechanism or another. This is not to say that nothing can be said under these conditions, but what CAN be said may be surprising.

Sure, evidence for Dark Matter can be cited. Something would be very wrong in Science if this were not so. For instance, the Sunyaev-Zeldovich redshift modulation effect, the progressive S-Z effect that follows S-Z from void to void over great intervals of space & time, What I call the "MOND" effect1 and of course the Bullet Cluster effect.

The SN-1a data are used for establishing the claimed existence of Dark Energy due to acceleration of the Hubble expansion of the universe but, if the Friedmann equations can indeed be used when such large distances and long times are involved, and if the Cosmological Principle is strictly valid over these distances and times, and if the simplifying assumptions that are made in order to make calculations tractable are not too bad, then Dark Matter can be got by difference if the guesses for the total mass of the universe are valid. These are big "Ifs". And, there are too many of them for comfort.

I do not care to dispute Dark Energy. Dark Matter is my quarry. I do not even dispute the existence of Dark Matter, actually. I question whether its nature is "like" some kind of halo or cloud of "weakly interacting massive particles (WIMPs)" That is, unless WIMPS are as massive as black-holes, of course. It is unnecessary to postulate Dark Matter in this form. The effects can all be handled by the assumption of super-massive black-holes in the centers of spiral galaxies (the BH gravitational field enhanced by the galactic disk), dark black-holes in globular galaxies and offset distributions of black-holes in colliding globular galaxies and clusters of such like those seen in the Bullet Cluster. In all these cases, the 2D, graphically hyperbolic 1/r* gravitational field potential profile will explain it. Doing the math is on my agenda. But getting the spoken language description straight is key to getting started on doing this math.

r* = rR where R is the "value" of the unit vector associated with the r vector (r) but, R retains it dimensionality. This project is obviously still under development. I thank you because your comments stimulate me to express answers to questions that will certainly arise in the future from friends and critics alike.

1 The "MOND" effect includes the rotational anomalies seen in galaxy clusters and super-clusters.

40. Originally Posted by Gary Anthony Kent
Again, I ask you to actually show us how you propose to predict the rotation curve of any galaxy of your choice using your hyperbolic method. If you cannot do this, then you really do not have a theory.
This is what you mean eh? Why didn't you say so?
Aaaahhh. I get it, you are an attention troll.

41. Originally Posted by PhysBang
Originally Posted by Gary Anthony Kent
Again, I ask you to actually show us how you propose to predict the rotation curve of any galaxy of your choice using your hyperbolic method. If you cannot do this, then you really do not have a theory.
This is what you mean eh? Why didn't you say so?
Aaaahhh. I get it, you are an attention troll.
Aaawww! Name calling won't help.

Where shall I start? Shall I try to model Andromeda? We have lots of data. Maybe some other galaxies too, like NGC5856. Galaxies with different relative orientations would be nice.

I will eventually use a homogeneous nonlinear differential equation(s) derived, developed or stemming from the basic hyperbolic 1/r* gravitational force equation. I cannot afford Mathematica to solve it or them. But it should be simple to do manually.

In the meantime, I can use TK Solver Plus to make plots by brute blunt force. TK is much cheaper than Mathematica and is the one I used to make the graphs present at my website, LONETREE* PICTURES* &* NEW* COSMOS with MOND.

r* is r multiplied by the dimensioned numerical value of the unit vector associated with r, (r1). It keeps dimensional analysis sensible. It is justified for other fundamental reasons too, of course. Obviously, this project is still under construction.

42. I have prepared a "One-Sheet" for my lecture
on "The Fate of the Universe"

Many scientists have verified the fact that the Theory of General Relativity does indeed regard black holes as both physical realities and logical or mathematical subjects. Which means that they are real "point masses" (within Heisenberg limits) having infinite density and infinitely deep gravitational wells. This also means that they have a graphical mathematical "asymptotic" limiting boundary (to both the abscissa and ordinate) gravitational potential profile. As such, their overall physical geometry must be consistent with their nature as singularities, or else the term "singularity" has no meaning. Their actual gravitational potential profile must be represented by a hyperbola. This is HUGE! Just how huge is the subject of my lecture.

This lecture is a Power-Point presentation. It is meant for the general audience of persons desiring an edifying talk on a scientific subject.

I include many slides with beautiful graphics and photographs of a kind appropriate for a talk on astronomy. Stars, galaxies, planets, telescopes, people of science and their institutions, etc. Non-technical, it can be understood by any high school graduate.

I am a PhD level lecturer (graduated with a M.S. in physical science from I.I.T. in 1985) with a website http://www.lonetree-pictures.net, several popular blogs, respected participant in several scientific forums and a writer/editor for Wikipedia.

Sincerely,

Gary Kent

43. I submit my material to forums like this in order to get feedback in preparation of manuscripts for submission to journals for editors and referees to destroy.

44. Originally Posted by Gary Anthony Kent
Black holes are singularities. This means that they must exist as point masses, according to general relativity. The gravitational field around a point mass must have a hyperbolic potential profile, not a parabolic one as assumed by Newton’s Law of Gravity. This is because the event horizon of a black-hole is not a true surface like that of a planet or a surface zone like that of a star. The only characteristic of a black-hole that makes any difference here is the point-mass at the Heisenberg uncertainty constrained center. Mordechai Milgrom's work (see below) proves that there is more to a black-hole than just its event horizon.
Admit the hyperbolic black hole galactic gravitational field (HBHF) as a postulate

I have shown that it is expedient and practical to admit the hyperbolic black hole galactic gravitational field (HBHF) as a postulate – that is, as a mere tentative logical premise. There are several ways in which it could be confirmed as a contender for a place in the cosmological pantheon of physical “law”. If it could be seen as a real cosmic rule, every single one of the phenomena that are now ascribed to “Dark Matter” can be more parsimoniously charged to the HBHF. This is also because, by extension, the HBHF can be used to characterize the hyper-excited “inflaton particle” in the false vacuum of the ultra-high energy “inflaton field” that is supposed to have sprung into existence as a probabilistic quantum fluctuation. It offers a new way to forge another link between quantum dynamics and relativity theory.

When enough such links are made, we shall obtain a quantum theory of relativity without having to tolerate the putative overbearing “grand unified theories” or “theories of everything” like superstring theory or quantum loop gravity. These seem to offer no advantage other than the grandeur of hyper-complexity and the safe haven of unfalsifiability. In other words, the HBHF might allow theorists to “get real”. So, it is practical and expedient to admit the HBHF as just such a postulate.

The HBHF, if it can be allowed, would further reinforce Inflation Theory by providing a mechanism for the transition of the excited inflaton HBHF particle/field to a “ground state” inverse square gravitational field. It implies how potential energy in the inflaton field might have powered inflation and how it may now be powering “reinflation”, the accelerating Hubble expansion of the universe in the current epoch. It would seem to require endorsement of the “Many Worlds” interpretation of quantum mechanics/dynamics because the HBHF must have pre-existed inflation in a sort of “metatime” in a “multiverse”. But, this is implied by Alan Guth’s inflation hypothesis anyway. And then, if the universe was once a quantum entity, then it still is – with profound implications and more opportunities to forge links with GR.

Incidentally, the HBHF can certainly be admitted according to common interpretations of some theorems of general relativity if spacetime, in the moments before inflation, was indeed regarded as “flat”. That is, the HBHF can certainly be allowed by GR if the HBHF inflaton field is restricted to two dimensions. This gives a new twist to inflation. It may mean that inflation involved “unpacking” our spatially 3-D universe from a more compactified 2-D version.

And then, the deep interior of black holes at their singularities (as physical realities) might be viewed as recompactifications of spacetime – reconvolutions to a strictly 2-D format wherein the HBHF can persist with no contradiction to conventional interpretations of GR. Then, in our multiverse, the galactic 2-D HBHF sibling set might define orbital planes for each and every entity in its purview.

That this galactic field must be defined as a disk shaped oblate spheroid means that its tidal influence on the central super-massive Black Hole (SMBH) must be concentrated in the plane of the galaxy. The mass of the disk may be thousands of times the mass of the SMBH so, its (mutual) effects on the SMBH are very substantial. Thus, Einstein’s theory of the relativistic non-symmetric gravitational field must be used to characterize it and that of the SMBH. Nobody has ever done this. And Birkhoff’s Theorem or its congeners simply do not exactly apply to any real BHs.

Simple geometry is used to define radiant flux and other quantities that are posited to emanate from a point source. An imaginary sphere is constructed around the source. An infinitesimally small area is defined on the surface of this sphere. Then the flux, quantity of lines of force or light lines, through this fractional area must be proportional to 1/r2 because the total area of a sphere is proportional to 1/r2 and the spherical enclosure envelopes all the flux. Using this definition to prove that gravity must be an inverse square (1/r2) phenomenon uses circular reasoning because it assumes as a premise that which is to be proven.

What if the source, even though it is a point, is assumed to be enclosed by an infinitesimally small space that is a very oblate spheroid by virtue of its extremely rapid rotation? What if this is the ultimate source, in fact. Then, what if this flux emission pattern is also very strongly oblately spheroidal? In addition, what if this flux was influenced by relativistic “frame dragging” and “thirring”? Also, what if the gravitational tidal influence of a galactic disk would also influence this spheroid to be even more oblate? The gravitational field of the disk must be perfectly coaxial and concurrent with the field of the SMBH. Its field must perfectly superpose. Then, the combined field must be treated in order to determine if there could be a hyperbolic field component. But, this combined field is even more “non-symmetric” and even more difficult to handle with GR, except by Einstein’s non-symmetric field theory, which has never been done. So, it is really impossible to prove by appeal to any theory or principle whatever whether the hyperbolic gravitational field is impossible. But, it is possible to appeal to strong geometric principles to argue that, indeed, it is possible.

See more details at www.NeoCosmology.blogspot.com .

This reply is designed to show a prospective collaborator on a formal paper that it may be worthwhile to join me. Contact info is available in my profile. I am spreading this call for collaborators as far and wide as I can. The probability is small, so the broadcast must be large.

45. Gary. Making the same post in three threads could (and should) be considered SPAM!!!

I'd suggest you discontinue this practice.

46. This has been dealt with on another thread :

What Imbues the Higgs Boson with its Mass?

47. Originally Posted by MeteorWayne
Gary. Making the same post in three threads could (and should) be considered SPAM!!!

I'd suggest you discontinue this practice.

I had a specific purpose in mind. I wanted to include a call for collaborators on a formal paper, but I forgot to insert it. I fixed this. I think such a call should include a convincing description of what is being asked

48. Originally Posted by Markus Hanke
This has been dealt with on another thread :

What Imbues the Higgs Boson with its Mass?

Yes. I wonder if I forgot to add my call for collaborators there too. I will check. If I keep at it, I know I can find a good candidate.

49. But posting the same thing in 3 threads is SPAM.

50. Originally Posted by MeteorWayne
But posting the same thing in 3 threads is SPAM.
My call for collaborators must be broadcast as far and wide as possible for there to be even a small chance of a legitimate response.

51. But posting the same thing in 3 threads is SPAM.

52. Originally Posted by Gary Anthony Kent
Black holes are singularities. This means that they must exist as point masses, according to general relativity. The gravitational field around a point mass must have a hyperbolic potential profile, not a parabolic one as assumed by Newton’s Law of Gravity. This is because the event horizon of a black-hole is not a true surface like that of a planet or a surface zone like that of a star. The only characteristic of a black-hole that makes any difference here is the point-mass at the Heisenberg uncertainty constrained center. Mordechai Milgrom's work proves that there is more to a black-hole than just its event horizon.

The Hyperbolic Hyper-Massive Black-Hole Universe

See The Hyperbolic Hyper-Massive Black-Hole Universe and Galactic Gravitational Field (HHBF), which is a paper written for the blog http://garyakent.wordpress.com that describes the e-Model for inflationary expansion of the universe. The hyperbolic hyper-massive black-hole gravitational field is a phenomenological postulate, that is, it is a tentative premise that should be confirmed by experiment or observation and need not wait for theoretical justification. In the case of galaxies and galactic clusters, there is already enough observational support for the galactic hyperbolic super-massive black-hole gravitational field (HSBF).

The point is emphasized that Birkhoff’s Theorem and other interpretive principles derived from general relativity cannot apply to any real black-holes. These rules presume that the massive bodies that are considered are always “unperturbed” and are perfectly “spherically symmetric”. No real black hole meets these criteria. The rules are good only for approximate calculation, not for “precision cosmology”.

Besides, GR should not prohibit a gravitational field that declines as 1/r if a metric is found, similar to the Schwarzschild metric, using assumptions and boundary conditions wherein a singular black-hole is presumed at the outset. If such a gravitational field can be confirmed, the e-model will serve as more evidence for the existence of our universe as part of a multiverse in meta-time.

Hugh Everett may one day be seen as a thinker on a par with A. Einstein. And, John Archibald Wheeler’s suggestion concerning the quantum self-interference of probability density waves may be taken more seriously while Everett’s declaration of the “reality of probability” as a sort of substance gains credence.

Self-interference can explain the virtual absence of antimatter (AM) in our universe. AM would be confined to our virtual twin, which must exist according to the logical extension of Alan Guth’s inflation hypothesis wherein a virtual particle came into existence from a hyper-excited false vacuum which came to exist precisely because of its ultra-high energy level. It would be seen as the deeper mechanism behind apparent “symmetry breaking” and unbalanced annihilation of fundamental sub-nuclear particles and antiparticles to give our universe with matter as the dominant form.

The existence of an interference twin could also be helpful in explaining the hyperbolic field as the resultant of a superposition of states. As the only real (to us) expression of a statistical process within the multiverse, we experience only the total sum, the superposed probability density form from which emerges probability, P --> 1. There are ways that such a superposition might affect the shape of a gravitational potential well. Gravity itself may be viewed as a probability vortex or wave in the Einstein Aether. There is much that has not been considered.

53. Hugh Everett may one day be seen as a thinker on a par with A. Einstein.
Good grief.

54. Galactic M-Sigma Relation and the Anomalous Stellar Velocity Dispersion

Hypothesis: Supermassive black holes must develop incredibly high spin rates, as would be measured by an observer under the event horizon. They condense initially out of massive supernovae and then from stellar components that orbit in concert within the innermost stratum of the central bulge of spiral galaxies. Due to this ultra high spin rate, nearing infinite rate below the event horizon, matter in such black holes never has a chance to compactify to a singular point with virtually infinite density. Instead, it flattens not to a mere point mass or to a simple ring singularity, but to subtend a "planar" subset of spacetime that is only 2 dimensional. It becomes a huge flat spacetime disk. But, this spacetime parcel still has mass.

Oddly enough, this explains the strange correlation of the velocity distribution of stars in spiral galaxies wherein rotational v of outer stars correlates with the mass of the central supermassive black-hole, the M-sigma relation. There should be no such correlation if gravitational force for black holes is an inverse square central force. This notion shows that no exotic dark matter is needed to explain this phenomenon. But, Dark Matter is still implied by this hypothesis.

Because by extreme contraction under rapid spin of matter to "almost” a point singularity with "almost” infinite density (“almost” means “to below a Planck distance”), the gravitational force therein is so intense that it is asymptotic in behavior: it is hyperbolic (1/r) in nature and it changes the nature of spacetime. So, it emanates from an extensive centripetally induced 2-D “disk” singularity. A peculiar result is that for stars nearer the galactic periphery, stellar velocity v' = (GM/r*)½ , that is, it is a constant that is totally independent of r. (r* = the unit vector of r, for dimensional integrity.)

Therefore, it is actually observed (the M-Sigma relation and the anomalous velocity distribution in galaxies and clusters) that this hyperbolic 1/r gravitational field of the supermassive black hole disk singularity can reach to the galactic periphery and far far beyond. And, because it is so much more extensive than an inverse square force, it has an effect on other nearby galaxies which also may have supermassive black holes with similar gravitational forces in play. This possibility explains all the phenomena associated with Dark Matter. It does not deny Dark Matter. It clarifies it.

This massive flat relativistically plausible spacetime ultra-spin disk is a hyperboloid of one sheet. It has a saddle shape, its being embedded in a 3-D + time universe. The curvature of the hyperboloid does not become apparent until r becomes very large, far beyond a galaxy. So, to engage other galaxies with their own SBH hyperbolic fields, the "plane" or surface of this curved sheet will align with them more readily because it is not really planar or “flat”.

This alignment is a way to explain the observed large scale network or spiderweb distribution of galaxies within clusters and superclusters. It also helps account for the primordial structure of the universe, as supermassive black holes may have been very common in the beginning.

Newton’s law will accommodate a 1/r gravitational field only if spacetime is limited to 2 dimensions plus time, by general relativity. Kepler’s laws can be modified to accommodate a 1/r field because these laws assume Newton, and Newton’s law needs only to be rewritten for gravitational 1/r 2-D spacetime.

This 2-D spacetime parcel possesses mass, like the highly excited inflaton field postulated by Alan Guth. Also, since it is spacetime in nature, it is immune to the event horizon of a black hole. Therefore, it can extend as far outward as is necessary to account for its effects - the real meaning of infinity.

The potential energy profile of the hyperbolic 1/r supermassive black hole galactic gravitational field is generally higher than the profile of the equivalent inverse square profile. So, the difference between the P.E. of the hyperbolic field and the P.E. of the inverse square field is a real energy difference. Because M = E/c2, this difference represents mass – matter that is unseen and unseeable. That is, this is Dark Matter.

I have written a paper along these lines. But, I need a reviewer to help check my mathematics.

kentgen1@aol.com

55. I have an offer from the chief editor of a scientific journal to publish my paper on rapidly spinning black holes and their transformation of spacetime BELOW the event horizon to a two dimensional disk that, nevertheless, extends gravitationally beyond the horizon to far beyond a galaxy perimeter. It is important to note, as I do in my paper, that objects cannot experience a 2-D and a 3-D gravitational field simultaneously.

The 3-D field arises from the mass of the galactic bulge and all the material that has descended to the horizon where the relativistic time dilation effect will cause time to literally stop (from our perspective) and the in-fallen matter's gravitational field to become frozen. But, the 2-D field arises as an observable effect of the descent of this same matter/energy that, by its own experience of continuing time, progresses all the way to as near to the singularity as may be necessary to achieve the transformative spacetime phase change effect.

So, objects that orbit the central black hole in the plane of the galactic disk feel the coaxial 2-D, hyperbolic (1/r) gravitational field and objects that orbit chaotically within the bulge feel an inverse square (1/r2) field. So, measurements of central supermassive black hole mass that depend on Kepler's (3-D) laws to analyze the behavior of bulge stars should be correct. But, analysis of orbits of stars farther out in the disk should use the 2-D form of Newton's law and Kepler, wherein orbital velocity, v = (G*Mbh/r*)½ where G* is the 2-D gravitational constant and r* is the unit vector of r, for dimensional integrity.

Mbhs for any given central supermassive black hole found by the two different ways should agree. But, there is a problem. Orbital v is found to be "virtually" constant from galaxy to galaxy. And, if G* is constant then Mbh should be constant also. But this cannot be so. Then, Mbh and G* must be allowed to vary inversely. This is hard to support.

G* can found theoretically or from the anomalous velocity dispersion equation, above. This approach uses Mbh found from the M-sigma relation. This is essentially a (3-D) Keplerian method that uses stellar orbital velocity that encloses chaotic orbits of bulge stars that are at one standard deviation from the center. Then, G* = r*v2/Mbh. But, this implies that v and Mbh must vary inversely. The only way that this could be is for G* to be so small that variations in v cannot be precisely measured and have actually been overlooked.

The fact is, G* is seen to be many orders of magnitude smaller than G, when this calculation is performed. This means that if v is measured more carefully, it should be found to vary as predicted here. This value for v, usually called σ (sigma), must not include contributions from the orbits of stars that are mainly in the plane of the galactic disk, for these stars will be under the influence of the hyperbolic (1/r) supermassive black hole gravitational field. Such stars will display effects of G*, not G. G* is the quantity that we would be trying to isolate, so such a calculation would contain a circular component. So, all the M-sigma relation data must be redone. This will take some time.

The universe is over 13.7 billion years old. So, what's another decade or so?

Gary A Kent

56. I have an offer from the chief editor of a scientific journal to publish my paper
Congratulations. What peer reviewed journal would that be?

achieve the transformative spacetime phase change effect
Cool. What's that?

... Ya know, I was going to do a line by line sarcastic reply to this post, but then I realized, after the first line, it would be totally redundant.

Empty word salad, devoid of meaning. This could have been done by a random sentence generator

57. Originally Posted by Gary Anthony Kent
{snip}
Hint: If you don't want to be written off as a crank right away, don't spam, and don't use zillion-point CRACKPOTFONT(tm). Legitimate authors never use this font. Crackpots frequently do, apparently believing that shouting is necessary to compensate for the fact that their ideas are themselves unconvincing.

58. So, objects that orbit the central black hole in the plane of the galactic disk feel the coaxial 2-D, hyperbolic (1/r) gravitational field and objects that orbit chaotically within the bulge feel an inverse square (1/r2) field.
This is trivially wrong, since neither is a correct description of gravitational physics in the vicinity of very massive objects with angular momentum. This is a scenario which needs to be treated under General Relativity, using the Kerr metric.
But perhaps you still wish to present your detailed maths here, so that we can show you exactly where you are going wrong.

Last warning

60. Stop spamming.