If you have two objects of equal mass, then what’s the closest distance that they can orbit at in terms of their schwarzschild radii? How fast would they be orbiting? What About stable orbits?
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If you have two objects with non-negligible mass there are no stable orbits due to loss of energy to gravitational radiation.
When one of the two mass is much smaller than the other, there may still be an approximate sense in which you talk about orbits and stable orbits. However, in the equal mass limit, the effect of dissipation is so strong in the strong field regime, that there is no sensible way to disentangle the conservative dynamics from the dissipative dynamics. All you have is inspirals.
