## Does the speed of moving object curve spacetime?

 Quote by tom.stoer The question is "Does the speed of moving object curve spacetime?". The approach is simple: we use the metric or geodesics to study spacetime curvature. Then we compare different mass distributions i.e. we study the effect of different mass distributions on geodesics.
The approach may be simple but as I said above if you are using a vacuum solution, the moving objects can only be test particles and there are no solutions in general relativity with test particle stress-energy.

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 Quote by yuiop This is in direct contradiction to ...
It isn't; it's simply an approximation to study a collapse w/o any change in internal d.o.f., radiation etc. A collapsing sphere of dust w/o pressure is certainly only an approximation, therefore your hybrid version taking other effects into account is better.

All what I am saying is that during the collaps where the pressureless dust is a good approximation we have "kinetic energy" that does not affect spacetime (outside the initial sphere of dust).

 Quote by TrickyDicky Maybe you haven't noticed (you may want to take a look at the Beyond the Standard model subforum for instance), but there's close to consensus among scientists about considering GR an extremely good approximation to the universe we live in , but obviously not "the theory", as in the ultimate theory, there are clearly situations that are outside of the scope of GR and that don't describe the universe we live in. , regardless of your considering it silly or not.
We are talking about a problem which can be asked, discussed and solved perfectly within GR; there's no need for any physics beyond GR.

 Quote by TrickyDicky There is simply no practical exact solution of the EFE that deals with many-body problems. That has been known since little after the time Einstein came up with the EFE. There are no solutions in general relativity with test particle stress-energy.
We don't need this. I presented a couple of scenarios where motion is not due to "n-body solutions" but due to internal d.o.f., i.e. part of the stress-energy tensor. That's perfectly valid and we even have solutions for these scenarios.

 Quote by TrickyDicky The approach may be simple but as I said above if you are using a vacuum solution, the moving objects can only be test particles and there are no solutions in general relativity with test particle stress-energy.
I am not proposing a vacuum solution. A collapsing dust is not a vacuum solution; the Neugebauer–Meinel disk is not a vacuum solution. I am not discussing "test-particle-stress-energy" but I use geodesics of test particles to analyze these non-vacuum spacetimes; that's a big difference.

 Quote by tom.stoer We don't need this. I presented a couple of scenarios where motion is not due to "n-body solutions" but due to internal d.o.f., i.e. part of the stress-energy tensor. That's perfectly valid and we even have solutions for these scenarios.
Your scenarios might be fine by themselves, I'm not debating that, I'm saying they don't address the OP at least the way it is written. The OP talks about a body not about a perfect fluid dust solution.
 Quote by tom.stoer I am not proposing a vacuum solution. A collapsing dust is not a vacuum solution; the Neugebauer–Meinel disk is not a vacuum solution. I am not discussing "test-particle-stress-energy" but I use geodesics of test particles to analyze these non-vacuum spacetimes; that's a big difference.
Again, the OP was about the motion of a body. Not a fluid.

 Quote by tom.stoer We are talking about a problem which can be asked, discussed and solved perfectly within GR; there's no need for any physics beyond GR.
What problem are you referring to? the OP's or your dust solutions? The latter are of course within GR.
And by the way by proposing fluid solutions you are implicitly admitting what I said about n-bodies and GR, in that case I don't know why you support yuiop on this.

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 Quote by TrickyDicky Again, the OP was about the motion of a body. Not a fluid.
As far as I know, people can and have done two body numerical computer simulations of colliding black holes, based on GR without introducing any new "beyond the standard model" theories.

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 Quote by TrickyDicky Your scenarios might be fine by themselves, I'm not debating that, I'm saying they don't address the OP at least the way it is written. The OP talks about a body not about a perfect fluid dust solution. Again, the OP was about the motion of a body. Not a fluid. What problem are you referring to? the OP's or your dust solutions? The latter are of course within GR. And by the way by proposing fluid solutions you are implicitly admitting what I said about n-bodies and GR, in that case I don't know why you support yuiop on this.
TrickyDicky, what else but a localized fluid or dust should a "body" be?

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 Quote by yuiop As far as I know, people can and have done two body numerical computer simulations of colliding black holes, based on GR without introducing any new "beyond the standard model" theories.
That's correct, but as I said above the black holes are in a sense not very good examples of "bodies". The are vacuum solutions. Nevertheless you are right, there are simulations of colliding black holes. One can show that the system emits gravitational waves i.e. propagating curvature.

 Quote by yuiop As far as I know, people can and have done two body numerical computer simulations of colliding black holes, based on GR without introducing any new "beyond the standard model" theories.

 Quote by tom.stoer That's correct, but as I said above the black holes are in a sense not very good examples of "bodies". The are vacuum solutions. Nevertheless you are right, there are simulations of colliding black holes. One can show that the system emits gravitational waves i.e. propagating curvature.

I've been careful in all my replies to make clear the caveat that there's linerization approaches that have more to do with approximmating a flat newtonian solution than with the gravity as curvature of spacetime approach of the "full" nonlinear GR.

 Recognitions: Science Advisor Neither the BH collisions (afaik) nor the physical solutions like fluid or dust (here I am sure) rely on Newtonian approximation.

 Quote by tom.stoer Neither the BH collisions (afaik) nor the physical solutions like fluid or dust (here I am sure) rely on Newtonian approximation.
BH collissions do , certainly fluid solutions don't, I never said they did, I said the way the OP was written I interpreted it as a vacuum solution scenario, I might have interpreted it wrong.
 Quote by tom.stoer TrickyDicky, what else but a localized fluid or dust should a "body" be?
The way I understood the OP, he seemed to be talking about the motion of a discrete moving object, a point particle or test body, such objects are idealizations and by definition have no internal structure. This is the way this is usually discussed in the context of vacuum solutions.

Now, you claim the OP problem is not a vacuum problem and in that case of course we could talk about localized dust particles much in the same way galaxies are considered localized particles of a dust in FRW cosmologies, but in those cases the particles of the dust are infinite in number as points of a continuous pressureless fluidbut then again the OP said "we have an object....".

 Recognitions: Science Advisor I think we agree that interpreting it as a pointlike or test particle does not make sense. So my idea was to discuss a context in which the question could make sense.

 Quote by tom.stoer I think we agree that interpreting it as a pointlike or test particle does not make sense.
I'm sure we agree about many things
Honestly, I think we are in the semantic, interpretational camp right now (maybe the OP could clarify what he meant), if he really meant how the speed of an isolated body affects the curvature of spacetime I really think there is no answer within relativity.
 Quote by tom.stoer So my idea was to discuss a context in which the question could make sense.
This is always a practical thing to do, as long as we are answering the problem asked, otherwise it is sometimes more honest to answer that the question may not have a clear answer in the context it was made.
We don't want to be like the drunk guy in that old joke that was looking for his keys at night near a streetlamp just because there was more light there not because he had lost them anywhere near the streetlamp.

 Tags dilation, gravitational, mass, relativistic, velocity