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Would there be any implicit differences between (A) a two-body metric where the two central masses are drawn ever further together, with angular momentum included, and (B) the Kerr metric? Angular momentum would still be part of the system, but it would be explained by a more intuitive form rather than the assumption that mass inherently has angular momentum. It would also allow for symmetry breaking if one desired, as the closer to the center of the coordinate system you become, the more apparent other subsystems could be. This would allow a sort of binary-splitting capability into the metric, allowing one to explore the events near the center in more detail than simply having everything fall towards some mysterious rotating mass at the center.

Of course, it would be extremely difficult to formulate this explicitly in all possible details, but that's always the case with models of the universe. It's a step up from the Kerr metric though.

If I were to start deriving the metric, I would base it in bispherical coordinates and have the focal distance parameter "a" evolve with time, as well as the relative azimuthal angle as the central bodies orbit each other. What wouldn't be included is the effect that the test mass would have on the orbit of the central bodies, but we could assume that's so small as to not be relevant.

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# Two-mass Schwarzschild metric instead of Kerr metric?

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