Another paper (alas, poorly written due to ESL issues), by an independent author examines the difference between General Relativity and Newtonian gravity in the case of two massive bodies rather than one massive body and a test particle of negligible mass.
The result, analytically determined, confirms Deur's analysis that the distinction is not immaterial in some circumstances, and that this could be the underlying mechanism of modified Newtonian dynamics.
The metric tensor in the four dimensional flat space-time is represented as the matrix form and then the transformation is performed for successive Lorentz boost. After extending or more generalizations the transformation of metric is derived for the curved space-time, manifested after the synergy of different sources of mass. The transformed metric in linear perturbation interestingly reveals a shift from Newtonian gravity for two or more than two body system.
Shubhen Biswas, "The metric transformations and modified Newtonian gravity" arXiv:2109.13515 (September 28, 2021).
2 comments:
Equation 36 is the weird one.
To me - after reading for like 2 mins - it seems the author is trying to add two metrics together, using linearized theory, which should work well for say something like the Earth - Moon system (but where both the Earth and Moon are at rest).
I have not followed it through. Seems to me there should be no third term, but as the author says, that is the surprise.
I appreciate your analysis.
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