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Thread: Black holes not pathways

  1. #1 Black holes not pathways 
    Forum Freshman √-1human's Avatar
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    Black holes have a highly dense centre, singularity.People say that black holes are pathways like wormholes to other universes. But doesn't a black hole have a solid centre rather than a pathway, isn't singularity a highly dense solid centre .So all the matter that enters is just going to the highly dense centre of a black hole.So then black holes aren't a pathway, but just a compressor.Isn't it?


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    Brassica oleracea Strange's Avatar
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    No.

    ...

    Oh, you want more? That simplistic view doesn't really work because, with our current model, there is nothing to stop the collapse. So it isn't a small, dense solid core. It is a zero sized, infinitely dense point (that is kind of what singularity means in this context). Now, I don't think anyone really believes that is what happens. But we don't currently have an alternative model.

    As to the wormhole thing. That applies to certain types of black holes. But, again, who knows if it is physically realistic?
    Kerr black hole


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    Quote Originally Posted by Strange View Post
    No.

    ...

    Oh, you want more? That simplistic view doesn't really work because, with our current model, there is nothing to stop the collapse. So it isn't a small, dense solid core. It is a zero sized, infinitely dense point (that is kind of what singularity means in this context). Now, I don't think anyone really believes that is what happens. But we don't currently have an alternative model.

    As to the wormhole thing. That applies to certain types of black holes. But, again, who knows if it is physically realistic?
    Kerr black hole
    Interesting, i mean i didn't know a black hole had zero size.. I thought our comprehension of what matter would do when densely compacted like that is beyond mass. No core, but a different type of vacuum in there, which in turn could lead somewhere else, a higher energy plane of existence maybe.

    However, i do know that the energy output doesn't add up, the mass actually vaporizes in the black hole, so where does the energy go?

    A singularity in my idea is, a point in space-time where normal rules of physics do not apply, where behavior can not (yet) be predicted.
    Growing up, i marveled at star-trek's science, and ignored the perfect society. Now, i try to ignore their science, and marvel at the society.

    Imagine, being able to create matter out of thin air, and not coming up with using drones for boarding hostile ships. Or using drones to defend your own ship. Heck, using drones to block energy attacks, counterattack or for surveillance. Unless, of course, they are nano-machines in your blood, which is a billion times more complex..
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    Quote Originally Posted by Zwolver View Post
    Interesting, i mean i didn't know a black hole had zero size..
    Note that it is the singularity that has zero size. The black hole is defined by the event horizon which has a well-defined finite radius.

    I thought our comprehension of what matter would do when densely compacted like that is beyond mass. No core, but a different type of vacuum in there, which in turn could lead somewhere else, a higher energy plane of existence maybe.
    We don't know what happens. It almost certainly isn't a zero-sized point of infinite density.

    However, i do know that the energy output doesn't add up, the mass actually vaporizes in the black hole, so where does the energy go?
    Not sure what you are thinking of there? The mass and energy that goes into a black hole stays there as the the mass of the black hole. (Apart from the tiny amount that is lost by Hawking Radiation.)

    A singularity in my idea is, a point in space-time where normal rules of physics do not apply, where behavior can not (yet) be predicted.
    That is about right. The fact we get infinities (a singularity) is a good indication that the model is no longer applicable.
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    I was told that the pathway idea got its start due to a mathmatical issue. Apparently if you add rotation to the formula that discribe a black hole you come out with math that suggests a toroidol shape, like a donut.
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    Quote Originally Posted by Sealeaf View Post
    Apparently if you add rotation to the formula that discribe a black hole you come out with math that suggests a toroidol shape, like a donut.
    Would you have a reference for this ? I never associated anything in the Kerr metric with a torus.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Sealeaf View Post
    Apparently if you add rotation to the formula that discribe a black hole you come out with math that suggests a toroidol shape, like a donut.
    Would you have a reference for this ? I never associated anything in the Kerr metric with a torus.
    I think Sealeaf might be referring to the ring singularity.
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    Quote Originally Posted by dan hunter View Post
    I think Sealeaf might be referring to the ring singularity.
    Ah ok, I see what you mean. That's not a torus though, it's a 1-dimensional ring.
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    Yeah, but that is Sealeaf too.
    Last edited by dan hunter; March 23rd, 2014 at 08:26 AM.
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  11. #10  
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    Quote Originally Posted by Strange View Post
    The mass and energy that goes into a black hole stays there as the the mass of the black hole.
    It's worth saying that the mass at the central singularity can be removed by a change in the topology from topological flatness to a wormhole of zero-sized throat. This doesn't change the metric so that external observers observe the same mass for the blackhole. However, the collapse of matter may be considered as a continuous deformation that by definition does not change the topology. Since the non-collapsed matter is presumably topologically flat, the resulting blackhole is also presumably topologically flat. But the Schwarzschild blackhole is obtained by solving the Einstein equation with zero source term, thus strictly speaking describing the wormhole topology.

    Consider the following two-dimensional metric:



    This is a wormhole of throat-size . The Gaussian curvature is everywhere negative. The integral of the Gaussian curvature is a topological invariant and therefore invariant to continuous deformations. Interestingly, the metric can be continuously deformed to . But corresponds to the metric:



    which is the metric of a flat surface under polar coordinates. However, the thing to note is that deforming the wormhole to zero size never actually removes the wormhole. Even at , the wormhole persists as a point of infinite negative curvature. Nevertheless, it is metrically indistinguishable from a flat surface. In other words, the point of infinite negative curvature is mathematically invisible.

    In the case of a blackhole, the Einstein tensor that was the original matter that collapsed is also mathematically invisible. However, in this case, the Weyl tensor that is the gravitation increases without bound as the central singularity is approached, and this is evident within the metric.
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    Quote Originally Posted by KJW View Post
    It's worth saying that the mass at the central singularity can be removed by a change in the topology from topological flatness to a wormhole of zero-sized throat. This doesn't change the metric so that external observers observe the same mass for the blackhole. However, the collapse of matter may be considered as a continuous deformation that by definition does not change the topology. Since the non-collapsed matter is presumably topologically flat, the resulting blackhole is also presumably topologically flat.
    Hmm.. Why is it flat? Could it be that the atomic decay is so uniform this lines up perfectly to a point of least energy? This may cause it to follow predictable rules of physics anyway. I used atomic decay in a way because i think that matter (or the gravitational/electromagnetic/etc..) rotates, and when it is close enough (compressed), it rotates together, and rotation causes a 2D disk that is nearly infinitely flat.

    Could it be true?
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    Quote Originally Posted by KJW View Post
    topological flatness
    Come to think of it, I must admit that I am not really sure I understand the precise meaning of the term "topological flatness", and the textbook definitions I found are so cryptic that I can't really make heads or tails of them. Would you have a simple, intuitive explanation for this concept, by any chance ?
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by KJW View Post
    topological flatness
    Come to think of it, I must admit that I am not really sure I understand the precise meaning of the term "topological flatness", and the textbook definitions I found are so cryptic that I can't really make heads or tails of them. Would you have a simple, intuitive explanation for this concept, by any chance ?
    Take an infinite flat sheet and continuously deform it in any way (no tearing, joining or other discontinuous operations). The sheet will remain topologically flat. I should remark that the technical phrase is "homotopy equivalent to a flat space".

    Here's an example of the homotopy equivalence between a coffee cup and a doughnut:

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    Quote Originally Posted by KJW View Post
    Take an infinite flat sheet and continuously deform it in any way (no tearing, joining or other discontinuous operations). The sheet will remain topologically flat.
    So is the initial "flatness" of the sheet you start with the geometric notion of flatness, i.e. does it require a connection and a metric to determine flatness, or do you determine topological flatness in some other way ? It doesn't seem as if it could possibly be defined through curvature tensors, since those will not generally remain invariant under deformations.

    I do understand that the topology of course remains the same under continuous deformations.

    Basically, I am after the difference between "geometric flatness" and "topological flatness".
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    From a lingual view topological flatness would indicate Scientifically comparative flatness. So we would perceive it as flat, because of lack of comparison.
    Growing up, i marveled at star-trek's science, and ignored the perfect society. Now, i try to ignore their science, and marvel at the society.

    Imagine, being able to create matter out of thin air, and not coming up with using drones for boarding hostile ships. Or using drones to defend your own ship. Heck, using drones to block energy attacks, counterattack or for surveillance. Unless, of course, they are nano-machines in your blood, which is a billion times more complex..
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  17. #16  
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by KJW View Post
    Take an infinite flat sheet and continuously deform it in any way (no tearing, joining or other discontinuous operations). The sheet will remain topologically flat.
    So is the initial "flatness" of the sheet you start with the geometric notion of flatness, i.e. does it require a connection and a metric to determine flatness, or do you determine topological flatness in some other way ? It doesn't seem as if it could possibly be defined through curvature tensors, since those will not generally remain invariant under deformations.

    I do understand that the topology of course remains the same under continuous deformations.

    Basically, I am after the difference between "geometric flatness" and "topological flatness".
    In general, you would start with a space for which the Riemann tensor is zero. Then from any connection of that flat space, you would apply continuous deformations generated by arbitrary . If you can reach the target connection (or a coordinate transformation of the target connection), then the target connection is "topologically flat" (homotopy equivalent to a flat space) (alternatively, you could start from the target and continuously deform to the flat space). The target space will in general not be geometrically flat (because the deformations have introduced curvature). For an even-dimensional space, the volume integral over the entire space of:



    is a topological invariant (invariant to deformations by )1. This quantity will be zero for a topologically flat spaces though the converse is not true (e.g. a torus is not topologically flat even though this topological invariant is zero).


    1 This is true for Riemannian geometry. I don't know if it extends to non-Riemannian geometry (non-zero torsion, etc)
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    Quote Originally Posted by KJW View Post
    alternatively, you could start from the target and continuously deform to the flat space
    Ok, this makes sense ! So basically if something can be continuously deformed into a flat sheet ( and vice versa ), it is considered topologically flat. Right ?

    The target space will in general not be geometrically flat (because the deformations have introduced curvature).
    Yes, that's what I thought, and it makes perfect sense.

    For an even-dimensional space, the volume integral over the entire space of:



    is a topological invariant (invariant to deformations by )1.
    Very interesting !

    This quantity will be zero for a topologically flat spaces though the converse is not true
    Ok, got it, very handy to know. Thank you for the explanations !
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    Quote Originally Posted by KJW View Post
    In general, you would start with a space for which the Riemann tensor is zero. Then from any connection of that flat space, you would apply continuous deformations generated by arbitrary . If you can reach the target connection (or a coordinate transformation of the target connection), then the target connection is "topologically flat" (homotopy equivalent to a flat space) (alternatively, you could start from the target and continuously deform to the flat space).
    However, the discussion in post #10 indicates that it's not as straightforward as that.
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    Quote Originally Posted by Markus Hanke View Post
    Ok, this makes sense ! So basically if something can be continuously deformed into a flat sheet ( and vice versa ), it is considered topologically flat. Right ?
    That's basically it. However, I should point out that topology is not a strong suit for me and the subject is far more complicated than what I have described.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by KJW View Post
    Although not especially related to the topic, one thing I did discover is that the local quantity (not the volume integral):



    is everywhere zero for the FLRW metric of a constantly expanding flat universe. The thing that interests me about this is that introduces a notion in four (or more) dimensional spaces that has no correspondence in two dimensional spaces: that a non-flat space can exhibit no tendency towards deviating from topological flatness anywhere.
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    Quote Originally Posted by KJW View Post
    That's basically it. However, I should point out that topology is not a strong suit for me and the subject is far more complicated than what I have described.
    I understand, but this does at least give me the basic idea of what "topological flatness" means, and how it differs from the geometric notion of flatness. And it is quite intuitive.
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    But now it is said that there can't be an event horizon
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    However there can never be an infinitely dense point as, if there is one, the whole space-time continuum of the entire universe ruptures, so we can only say about a near to infinite core, present there, solid, ever so lightly.Einstein himself said that only two things are infinite the universe and human folly but then said that he was not sure that the former was infinite.We now be sure that the universe is not infinite but expanding, and whatever is infinite and still expanding cannot occur as infinity is the maximum point of expansion. So there can never be an infinitely dense substance, Oppenheimer when coining his ideas,thought about an object decreasing it's radius lesser than the Schwarzchild radius and not one with an infinitely densely core. But in the present model, a black hole is the opposite of the big bang in the inflatory model, the big bang gives a highly dense core exploding and rapidly increasing, but still only highly dense, and black holes are the opposite and has smaller highly dense core, but rather than expanding afterwards it decreased rapidly after the explosion of the star. So there is a dense core present.
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    Quote Originally Posted by √-1human View Post
    However there can never be an infinitely dense point as, if there is one, the whole space-time continuum of the entire universe ruptures
    Evidence?

    We now be sure that the universe is not infinite but expanding
    Really?

    and whatever is infinite and still expanding cannot occur as infinity is the maximum point of expansion
    What's infinity +1? Infinity +3,000? Infinity x 3,000?

    So there can never be an infinitely dense substance
    It may not be a substance as such, but you're reaching. Again.

    But in the present model, a black hole is the opposite of the big bang in the inflatory model, the big bang gives a highly dense core exploding and rapidly increasing, but still only highly dense, and black holes are the opposite and has smaller highly dense core, but rather than expanding afterwards it decreased rapidly after the explosion of the star. So there is a dense core present.
    Whut?
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    Quote Originally Posted by √-1human View Post
    However there can never be an infinitely dense point
    Remember that the singularity arises only because the domain of our current theory of gravity ( General Relativity ) is purely classical, i.e. it does not account for quantum effects. A gravitational collapse is a process where such effects need to be taken into account, which is why we currently get infinities. Once we have a fully consistent model of quantum gravity, it is reasonable to expect these singularities to vanish.

    Btw, nice avatar
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    Quote Originally Posted by Dywyddyr View Post
    Quote Originally Posted by √-1human View Post
    However there can never be an infinitely dense point as, if there is one, the whole space-time continuum of the entire universe ruptures
    Evidence?

    We now be sure that the universe is not infinite but expanding
    Really?

    and whatever is infinite and still expanding cannot occur as infinity is the maximum point of expansion
    What's infinity +1? Infinity +3,000? Infinity x 3,000?

    So there can never be an infinitely dense substance
    It may not be a substance as such, but you're reaching. Again.

    But in the present model, a black hole is the opposite of the big bang in the inflatory model, the big bang gives a highly dense core exploding and rapidly increasing, but still only highly dense, and black holes are the opposite and has smaller highly dense core, but rather than expanding afterwards it decreased rapidly after the explosion of the star. So there is a dense core present.
    Whut?
    Ever herd of general relativity, Einstein's theory of gravity, Lorentz theory of effects of accelerated motion.If there ever is an infinite point it will affect the entire universe. An object, even not with infinite dense, exploded and created the universe we live in now, SO can't an infinitely dense point affect the entire universe and destroy. So there can never be anything infinite. anything infinite thing that I can think of now is decreasing size, as infinite size can occur.
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  28. #27  
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    Quote Originally Posted by √-1human View Post
    If there ever is an infinite point it will affect the entire universe.
    Yeah?

    An object, even not with infinite dense, exploded and created the universe we live in now
    Did it?

    SO can't an infinitely dense point affect the entire universe and destroy.
    Can it?

    So there can never be anything infinite.
    Supposition.

    anything infinite thing that I can think of now is decreasing size, as infinite size can occur.
    Really?

    More unsupported claims...
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    What comes out of the other side. It doesn't just go in on one end, & nothing happen on the other. Don't They shoot beams of light out of both ends.
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    Quote Originally Posted by Charles M ODonnell View Post
    What comes out of the other side. It doesn't just go in on one end, & nothing happen on the other. Don't They shoot beams of light out of both ends.
    If you're talking about black holes what goes in generally doesn't come out.
    And, no, they don't "shoot beams of light out of "both ends"".
    They don't have "ends" for one thing.
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    Quote Originally Posted by Charles M ODonnell View Post
    What comes out of the other side. It doesn't just go in on one end, & nothing happen on the other.
    There is no "other side"; stuff falls into a black hole and adds to its mass. The black hole expands and gets more massive and (oddly) less dense.

    Don't They shoot beams of light out of both ends.
    No, the polar jets come from the spinning disks of material being accelerated as it falls in (not from the black hole).
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Charles M ODonnell View Post
    What comes out of the other side. It doesn't just go in on one end, & nothing happen on the other.
    There is no "other side"; stuff falls into a black hole and adds to its mass. The black hole expands and gets more massive and (oddly) less dense.

    Don't They shoot beams of light out of both ends.
    No, the polar jets come from the spinning disks of material being accelerated as it falls in (not from the black hole).
    Actually nobody knows what happens to stuff trapped in black holes. At least, stephen hawking claimed not to know, and i try not to get ahead of myself from now on.

    http://www.space.com/16867-black-hol...cs-theory.html

    And about the jets at the poles, something does seem to shoot out of it, i doubt it really does, but it looks like it, don't you think. From a telescope it even seems to move away from the poles. And if a black hole is flat (ish), then it could be mostly pulling from the circle around it, and then something could come out of it by the other ends. I'm just saying, you can't prove it doesn't, because there is no evidence for that. However there is evidence for possible quantum tunneling effect taking place around black holes, and possibly even inside it. (semi reliable source)

    Can Anything Escape from a Black Hole? | LiveScience
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    Imagine, being able to create matter out of thin air, and not coming up with using drones for boarding hostile ships. Or using drones to defend your own ship. Heck, using drones to block energy attacks, counterattack or for surveillance. Unless, of course, they are nano-machines in your blood, which is a billion times more complex..
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    Quote Originally Posted by Zwolver View Post
    Actually nobody knows what happens to stuff trapped in black holes.
    True. And I didn't say anything about that.

    And about the jets at the poles, something does seem to shoot out of it, i doubt it really does, but it looks like it, don't you think.
    It definitely doesn't. It comes from the accretion disk.

    And if a black hole is flat (ish)
    Which it isn't. Even a black hole with the fastest possible spin wouldn't be flat.

    I'm just saying, you can't prove it doesn't
    Yes you can. (Apart from quantum effects, such as Hawking radiation and tunnelling, which can be ignored as being too small.)
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Zwolver View Post

    I'm just saying, you can't prove it doesn't
    Yes you can. (Apart from quantum effects, such as Hawking radiation and tunnelling, which can be ignored as being too small.)
    I would like to see that citation though.
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  35. #34  
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    Quote Originally Posted by Zwolver View Post
    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Zwolver View Post

    I'm just saying, you can't prove it doesn't
    Yes you can. (Apart from quantum effects, such as Hawking radiation and tunnelling, which can be ignored as being too small.)
    I would like to see that citation though.
    Schwarzschild metric - Wikipedia, the free encyclopedia

    And of course, the same is true for other coordinate systems. For example: Waterfall
    Without wishing to overstate my case, everything in the observable universe definitely has its origins in Northamptonshire -- Alan Moore
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Zwolver View Post

    I would like to see that citation though.
    Schwarzschild metric - Wikipedia, the free encyclopedia

    And of course, the same is true for other coordinate systems. For example: Waterfall
    The first one, i knew, the second one, was surprisingly against your claim. It actually proved the exact opposite as what you were trying to prove.

    Which doesn't mean you are wrong, it just means that there are multiple ideas and theories, of which we don't know yet which one is best, or correct.
    Growing up, i marveled at star-trek's science, and ignored the perfect society. Now, i try to ignore their science, and marvel at the society.

    Imagine, being able to create matter out of thin air, and not coming up with using drones for boarding hostile ships. Or using drones to defend your own ship. Heck, using drones to block energy attacks, counterattack or for surveillance. Unless, of course, they are nano-machines in your blood, which is a billion times more complex..
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    Quote Originally Posted by Zwolver View Post
    The first one, i knew, the second one, was surprisingly against your claim. It actually proved the exact opposite as what you were trying to prove.
    How do you work that out? It says exactly the same thing (in a different way).

    Which doesn't mean you are wrong, it just means that there are multiple ideas and theories, of which we don't know yet which one is best, or correct.
    No. There is one theory (general relativity). Different coordinate choices give you the same result (they have to: they are describing the same thing).
    Without wishing to overstate my case, everything in the observable universe definitely has its origins in Northamptonshire -- Alan Moore
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    Quote Originally Posted by Zwolver View Post
    I'm just saying, you can't prove it doesn't
    You see, a very peculiar thing happens once you cross the event horizon - the radial coordinate changes its character and becomes time-like. What this means is that, as you age into your future, your radial position can only diminish, i.e. you get closer to the center of the black hole, no matter how and where you try to accelerate your rocket. Beyond the event horizon, you will always have the center of the black hole in your future, no matter what, because your local light cone is tilted inwards due to the geometry of space-time there. Hence there isn't any possibility for you to get back out, unless you can come up with some way to travel into your past
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Zwolver View Post
    I'm just saying, you can't prove it doesn't
    You see, a very peculiar thing happens once you cross the event horizon - the radial coordinate changes its character and becomes time-like. What this means is that, as you age into your future, your radial position can only diminish, i.e. you get closer to the center of the black hole, no matter how and where you try to accelerate your rocket. Beyond the event horizon, you will always have the center of the black hole in your future, no matter what, because your local light cone is tilted inwards due to the geometry of space-time there. Hence there isn't any possibility for you to get back out, unless you can come up with some way to travel into your past
    I'm not saying matter will get out. I'm saying there could be some type of particle, energy of an unexpected phenomena that goes the other way around.

    This also answers to Strange's post. The waterfall effect, painted multiple scenario's, of which some arrows pointed out of the center of the black hole..
    Growing up, i marveled at star-trek's science, and ignored the perfect society. Now, i try to ignore their science, and marvel at the society.

    Imagine, being able to create matter out of thin air, and not coming up with using drones for boarding hostile ships. Or using drones to defend your own ship. Heck, using drones to block energy attacks, counterattack or for surveillance. Unless, of course, they are nano-machines in your blood, which is a billion times more complex..
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    Quote Originally Posted by Zwolver View Post
    I'm not saying matter will get out. I'm saying there could be some type of particle, energy of an unexpected phenomena that goes the other way around
    As I said, the only way to get "back out" from a black hole is to travel into the past. There is no known particle or natural phenomenon which can do that.

    Explaining the "outward pointing" arrows in the diagram Strange has linked to isn't so easy; the basical upshot is that you need two patches of coordinates to cover the entire Reissner-Nordstroem space-time - one is our "normal" black-hole, the other patch is a corresponding white hole, which is in essence a time-reversed version of our black hole. Both of these patches belong to the same geometry, but they represent physically distinct regions of space-time. This works like so - matter falls into the Reissner-Nordstroem black hole; it initially speeds up, crosses a horizon, and then slows down due to the presence of electric charge. There is then a "turn-around point" where it comes to a stop, and transits over into the white-hole region. There, it speeds up again and gets ejected out of the white hole, which is not the same region of space-time where it initially fell in.

    This is effectively an electrically charged Einstein-Rosen-Bridge, however, it should be noted that tidal forces at the turn-around point become infinitely large, so any matter and information entering such a black hole will be crushed and destroyed; the wormhole is not traversable in any intuitive sense of the word. The space-time in the interior region of this construct is also not static, but fluctuates chaotically, further complicating this; note that this chaotic fluctuation isn't shown or mentioned in the simplified animated GIF.

    It should also be noted that the Einstein equations constrain only the local geometry of this solution, but not the global topology; this means there is no way to tell whether the white hole would be an asymptotically distant region of our own ( now multiply connected ) universe, or a separate region of a separate space-time manifold.
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    This is beyond my knowledge at the moment. I have no way to respond to this. A white hole is theoretical to my knowledge, i believe none of those are proven to exist.

    I will look into Reissner-Nordstroem black hole, Einstein-Rosen-Bridge and space-time manifold constructions. However i doubt i will ever grasp this math.
    Growing up, i marveled at star-trek's science, and ignored the perfect society. Now, i try to ignore their science, and marvel at the society.

    Imagine, being able to create matter out of thin air, and not coming up with using drones for boarding hostile ships. Or using drones to defend your own ship. Heck, using drones to block energy attacks, counterattack or for surveillance. Unless, of course, they are nano-machines in your blood, which is a billion times more complex..
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    Quote Originally Posted by Zwolver View Post
    I will look into Reissner-Nordstroem black hole, Einstein-Rosen-Bridge and space-time manifold constructions. However i doubt i will ever grasp this math.
    I can only advise to attempt to focus on the concepts and disregard the mathematics for now. This whole thing is one of the more non-intuitive aspects of General Relativity.
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