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- Let's say we have a massive body with an isometric gravitational field around it, described by the Schwarzschild metric. How would the field around it be different for a moving observer far away from the field?

Let's say we have some observer in some curved spacetime, and we have another observer moving relative to them with some velocity ##v## that is a significant fraction of ##c##. How would coordinates in this curved spacetime change between the two reference frames?

For example, imagine a massive body with an isometric gravitational field around it, described by the Schwarzschild metric. How would the field around it be different for a moving observer far away from the field? Would the field undergo length contraction, as with a Lorentz boost? Or is there some other transformation law we have to apply to curved spacetimes?

I know that changes in coordinate position transform differently between flat and curved spacetimes (i.e. Lorentz Transformations don't apply if you change position in a gravitational field), so I'm curious as to how gravitational fields change with motion. My intuition tells me that a gravitational field would experience length contraction and the like, as the spacetime far away from the body should behave approximately as if it was flat, and celestial bodies with gravitational fields still show evidence of relativistic effects.

So just how would coordinates in a curved spacetime change for an observer with relative motion?

For example, imagine a massive body with an isometric gravitational field around it, described by the Schwarzschild metric. How would the field around it be different for a moving observer far away from the field? Would the field undergo length contraction, as with a Lorentz boost? Or is there some other transformation law we have to apply to curved spacetimes?

I know that changes in coordinate position transform differently between flat and curved spacetimes (i.e. Lorentz Transformations don't apply if you change position in a gravitational field), so I'm curious as to how gravitational fields change with motion. My intuition tells me that a gravitational field would experience length contraction and the like, as the spacetime far away from the body should behave approximately as if it was flat, and celestial bodies with gravitational fields still show evidence of relativistic effects.

So just how would coordinates in a curved spacetime change for an observer with relative motion?

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