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Physics
Special and General Relativity
Gravitational Field Transformations Under Boosted Velocity
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[QUOTE="pervect, post: 6866219, member: 14402"] My computation, as well as being approximate, is coordinate specific. It more or less has to be, because force is not actually a tensor in GR. And the coordinate system of the analysis I did is that of a static observer, not a moving observer. The Aichelberg-sexl ultraboost would be a different coordinate choice and my analysis would not be directly comparable. The analysis in flat space-time, on Einstein's elevator, is much less problematic and more straightforwards. The relative acceleration between two nearby geodesics is well defined in a coordinate independent manner, using the geodesic deviation equation. Assembling these relative accelerations into a "force" requires assuming a specific coordinate system, a specific "chain" of observers, and a specific path to perform the integration. (Plus, along with all these assumptions, I made some simplifying approximations). It is interesting to compare the gravitational case to the much simpler electromagnetic case, the electric field of a moving point charge. See for instance [URL]https://www.physicsforums.com/threads/the-electric-field-of-a-moving-charge-according-to-purcell.909149/post-5736070[/URL]. Another poster, Bill K, tersley commented on the extra factor of gamma for the gravitational case as compared to the electromagnetic case in [URL]https://www.physicsforums.com/threads/field-of-moving-point-charge.563012/[/URL] [/QUOTE]
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Special and General Relativity
Gravitational Field Transformations Under Boosted Velocity
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