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.
Circular orbits in the extreme Reissner-Nordstr{\o}m dihole metric
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abstract
We study the motion of neutral test particles in the gravitational field of two charged black holes described by the extreme Reissner-Nordstr{\o}m dihole metric where the masses and charges of the black holes are chosen such that the gravitational attraction is compensated by the electrostatic repulsion. We investigate circular orbits in the equatorial plane between the two black holes with equal masses as well as the case of circular orbits outside this symmetry plane. We show that the first case reduces to an effective two-body problem with a behavior similar to a system described by the Reissner-Nordstr{\o}m spacetime. The main focus is directed to the second case with circular orbits outside the equatorial plane.
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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.