General relativistic three-body problem
Phys. Rev. D 114, 064053 – Published 11 September, 2026
DOI: https://doi.org/10.1103/3vyd-4jrb
Abstract
We examine analytically the restricted 3-body problem in general relativity for a set of extremally charged black holes. We apply the method of Ferrell and Eardley, which consists in perturbing the Majumdar-Papapetrou solution that describes a static set of such black holes. We extend the method from a pair of black holes to a triplet. We compare the motion of a test particle and a small black hole in the field of a rotating black hole binary and discover a repulsive self-force acting upon the third black hole.
