Circular orbits in the extreme Reissner-Nordstr{\o}m dihole metric

TL;DR

This paper analyzes the motion of neutral test particles in the gravitational and electromagnetic field of two charged black holes described by the extreme Reissner-Nordström dihole metric, focusing on circular orbits both in and outside the equatorial plane.

Contribution

It provides a detailed study of circular orbits in the extreme Reissner-Nordström dihole spacetime, including cases outside the symmetry plane, extending previous analyses.

Findings

Circular orbits in the equatorial plane reduce to an effective two-body problem.

Behavior of orbits outside the symmetry plane differs from the equatorial case.

The study highlights conditions for stable and unstable circular orbits.

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.