My question is very simple. Is energy is the CAUSE for bending of spacetime ? If yes how energy/mass is interacting/effecting the space time? If yes is it possible curvature of space time without energy. And does Einstein's equation tells about causation like in F=ma Force is the cause of acceleration .
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What level of study of general relativity have you done? (General because you are talking about bending.) Are you familiar, for example, with the Einstein field equations relating the Einstein tensor to the stress energy tensor? – BillOnne Jun 21 '22 at 19:59
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Matter and [non-gravitational] energy via the stress tensor can cause (or maybe better, “be associated with” [to purposely avoid or postpone the issue of "causation"]) spacetime curvature because the stress tensor is algebraically related to the Ricci curvature tensor, according to Einstein's field equation. So energy in a region of spacetime can be associated with some curvature in that region of spacetime.
However, spacetime curvature (more precisely, Riemann curvature) is composed of a part determined by Ricci curvature and the rest determined by Weyl (conformal) curvature (see Ricci decomposition). That is to say, one can have spacetime curvature (namely, Weyl-type curvature) without the presence of matter and [non-gravitational] energy. These are called "vacuum solutions" to the Einstein field equations.
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robphy
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Matter and energy can both distort spacetime, thereby producing gravity. Einstein's equations of general relativity make this relationship mathematically precise but do not explain why this occurs in and of themselves.
The closest to an explanation of "why" I have seen was in one of Steven Weinberg's books on physics, where he made the following point:
Einstein's equations of general relativity contain a prediction of something Weinberg called a gravitomagnetic field wherein if a circular platform that is not rotating about its axis in space were surrounded by a universe which was rotating about an axis aligned with the principal axis of symmetry of the platform, the gravitomagnetic field would be produced and would furnish to an observer on the platform all the effects he or she would experience if the universe was not rotating and instead the platform was- thereby guaranteeing the impossibility for the observer to determine whether it really was the universe that was rotating, or really the platform.
Weinberg then concludes with words to the effect that if it is true that one frame of reference is just as good as any other for the purposes of describing the dynamical behavior of the universe so long as you mock up gravity by applying accelerations, then the equivalence of all frames of reference requires the existence of gravity (i.e., general relativity)... for if this were not true then it would be possible to make a physical measurement that would reveal whether it was the universe or the platform that was rotating.
niels nielsen
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