Thread: what if schwarzchild solution were not exact?

they say Schwarzchild radius is an exact solution to Einstein's field equations.
Can you explain without math why and how this, and could you tell me what would happen if an experiment proved this is not exact, but wrong, say by a factor of 2?

field equations could be corrected or theory would simply collapse?

the easiest way to explain it is to picture<you can do this yourself,by drawing on paper>
draw a straight line..horizontally...now draw how mass curves the line,and you get the familiar warping of space around mass...in a 2d format..
the schwarzchild radius is the point on the line,where the curve begins..
picture the curve from above,as a circle...the radius of the circle is said radius..so its directly proportional to the mass...hope this helps

Originally Posted by logic

they say Schwarzchild radius is an exact solution to Einstein's field equations.
Can you explain without math why and how this, and could you tell me what would happen if an experiment proved this is not exact, but wrong, say by a factor of 2?

field equations could be corrected or theory would simply collapse?

It is hard to explain this without using maths, as it is an exact mathematical solution to a set of equations. How this works is that, in general relativity, Einstein laid out a consistent but very complicated set of equations to describe the overall relationships between things like matter, energy, momentum etc, and what effects those parameters have on space and time in general.

But in order to apply those parameters to the universe around us, we need to be able to use them to set up a framework against which we can reference measurements in particular situations - this is known as a metric. The Schwarzschild metric solves Einstein's equations exactly, for the case of a spherical non-rotating mass in flat space.

The solution cannot be wrong, as it solves all of Einstein's equations exactly. It is a mathematical concept, in the same way that is a solution that exactly describes the ratio between the radius of a circle and its diameter.

So, if experiment were to show that the Schwarzschild solution is incorrect, it would be showing that the field equations of general relativity were also incorrect.

Originally Posted by logic

they say Schwarzchild radius is an exact solution to Einstein's field equations.
Can you explain without math why and how this, and could you tell me what would happen if an experiment proved this is not exact, but wrong, say by a factor of 2?

field equations could be corrected or theory would simply collapse?

What would happen if an experiment proved that 2 was not a solution to x^2=4?

That's not really fair, since there are a number of assumptions made in the creation of the solution that mean that it is, in every application, an approximation, even though it is a mathematical solution of the field equations. If one observes deviations from the predictions of the solution, one can use these deviations to make more detailed measurements of mass distribution. Only in the most extreme case might we worry about the accuracy of general relativity.

this is essentially a matter of geometetry,ie the schwarzchild radius is the escape velocity,due to intrinsic properties of reflection.the energy level of the waveform,can be calculated as a proportional to the constant via incidence angle...it simply ever decreasing circles..re accuracy

Originally Posted by logic

they say Schwarzchild radius is an exact solution to Einstein's field equations.
Can you explain without math why and how this, and could you tell me what would happen if an experiment proved this is not exact, but wrong, say by a factor of 2?

field equations could be corrected or theory would simply collapse?

You can also derive the schwartzchild radius using a classical physics argument, although it's probably not rigorous to do so. With this in mind however i'd say that if an experiment measured a different radius to a black hole then it's more likely something went wrong with the experiment, measuring the boundary of a black hole directly would be a tricky prospect after all.

Originally Posted by PhysBang

1)What would happen if an experiment proved that 2 was not a solution to x^2=4?

2)That's not really fair, since there are a number of assumptions made in the creation of the solution that mean that it is, in every application, an approximation, even though it is a mathematical solution of the field equations. If one observes deviations from the predictions of the solution, one can use these deviations to make more detailed measurements of mass distribution. Only in the most extreme case might we worry about the accuracy of general relativity.

1) that is meaningless per se, and a fallacy, a false analogy. 2²=4 is an equivalence, a tautology, a synonym. It is a logical truth, is true for every proposition PhysBang is[=] PhysBang cannot be disproved by any experiment

2) that is irrelevant, and rather confused, and does not correspond to the question.
You have a theory founded on a set of field equations (rather complex , so there is no need to analyze them) , on the other hand you have
a formula describing the *effects of this theory in real world , which is the exact solution to those equations and
an experiment that shows the formula must be corrected by a factor of 2

someone already affirmed the theory collapses, is not mendable, can anyone disprove that with valid arguments?

*wallaby, I am referring to an observable experiment: deflection of light in presence of a G-field

Originally Posted by logic

someone already affirmed the theory collapses, is not mendable, can anyone disprove that with valid arguments?

*wallaby, I am referring to an observable experiment: deflection of light in presence of a G-field

The theory may collapse if the experiment shows the Schwarzschild solution is actually incorrect. The question is, how is the data being interpreted, in order to show it is the formula that needs a correction, rather than an incorrect assumption about some parameter in the analysis of the data?

So, how is the analysis deriving the Schwarzschild radius of the object in question, and why is the result incorrect by a factor of 2?

Originally Posted by logic

someone already affirmed the theory collapses, is not mendable, can anyone disprove that with valid arguments?

The theory would not collapse. The principles of general relativity have been tested and retested with experiments of much higher precision than we could hope to achieve with observational data on black holes. If someone did perform a measurement of the schwartzchild radius of a black hole that differed significantly from the calculated value, then provided they didn't fudge up the experiment or the calculations all it would imply is that the schwartzchild solution to the Einstein Field Equations was wrong (by either a little or a lot), the equations are not the correct application of General Relativity to a black hole or they provide an incomplete treatment of black holes.

Remember that General Relativity considers a black hole to be a large gravitational well from which light cannot escape and that astronomical observations have found what we believe to be such objects. If someone measured the schwartzchild radius of these objects to differ from their calculated values we might equally wonder if they are in fact black holes.

The evidence confirming general relativity as an explanation to gravitation is too substantial to outright discard the theory. That and the other explanations for why a different schwartzchild radius might be measured make it highly unlikely that the theory of relativity would collapse.