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I have been extensively studying General Relativity for some time now. Recently I asked myself a question which I can't answer.

If the gravitational metric is determined by the Energy content of the space, then any form of movement would alter the metric like the two body problem for comparable mass, for example.

I also read that, if the test mass is small enough, it is alright to describe its motion around a central mass using the geodesic equation, but what if the masses are comparable or equal?

Back to the two body problem, the masses move according to each others gravitational field, but by moving they alter their surrounding spacetime which also changes how the masses move in space, etc. However, can't I just say that the two masses are moving in a geodetic path described by a time dependent metric?

Lacking in the required fields of mathematics, I can't find the answer. I'm however more interested in a proof or citation if it exists rather than a simple yes or no for an answer. I would very much appreciate it.

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You are quite correct. For a system of two bodies the metric will be time dependant, and calculating a geodesic has to take into account the time dependance.

With a few exceptions, time dependant metrics are even harder to calculate than time independant metrics. For example the merger of two black holes has to be studied by numerical calculations and isn't fully understood even today. That's why we use time independant approximations if at all possible. Your example of a small test mass is one where a time indepenant treatment is usually good enough, even though strictly speaking the orbiting test mass will perturb the metric and make it time dependant.

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