In the Majumdar-Papapetrou two-black-hole spacetime, the mass ratio of the two holes divides into four regimes separated by three critical values that control the existence and topology of stable circular orbits.
Collinear solution to the general relativistic three-body problem
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abstract
The three-body problem is reexamined in the framework of general relativity. The Newtonian three-body problem admits Euler's collinear solution, where three bodies move around the common center of mass with the same orbital period and always line up. The solution is unstable. Hence it is unlikely that such a simple configuration would exist owing to general relativistic forces dependent not only on the masses but also on the velocity of each body. However, we show that the collinear solution remains true with a correction to the spatial separation between masses. Relativistic corrections to the Sun-Jupiter Lagrange points L1, L2 and L3 are also evaluated.
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Effect of a second compact object on stable circular orbits
In the Majumdar-Papapetrou two-black-hole spacetime, the mass ratio of the two holes divides into four regimes separated by three critical values that control the existence and topology of stable circular orbits.