That test particles travel along the geodesic is assumed in the context of GR. But does it apply to strongly gravitating object, such as black hole in an expanding universe, binary neutron star, etc.? How to justify if so?
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$\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$– Community BotCommented Jun 16, 2023 at 14:05
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$\begingroup$ Non-test objects in background fields do not move along geodesics due to the backreaction, and obey approximative equation of motions with backreaction included such as the MiSaTaQuWa equation. $\endgroup$– SlereahCommented Jun 16, 2023 at 14:10
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$\begingroup$ @Slereah Thanks for the key word 'back reaction' and MiSaTaQuWa equation. Now I know what to look for while dealing with related problems! $\endgroup$– BababelumaCommented Jun 16, 2023 at 14:36
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