On the equilibrium of a charged massive particle in the field of a Reissner-Nordstr\"om black hole

TL;DR

This paper provides an exact perturbative solution to the Einstein-Maxwell equations describing a charged massive particle at rest near a Reissner-Nordström black hole, revealing detailed metric and electromagnetic field expressions.

Contribution

It offers the first exact analytic perturbative solution for a two-body system involving a charged particle and a Reissner-Nordström black hole at rest.

Findings

Closed-form expressions for metric and electromagnetic fields

Inclusion of electromagnetically induced gravitational perturbations

Inclusion of gravitationally induced electromagnetic perturbations

Abstract

The multiyear problem of a two-body system consisting of a Reissner-Nordstr\"om black hole and a charged massive particle at rest is here solved by an exact perturbative solution of the full Einstein-Maxwell system of equations. The expressions of the metric and of the electromagnetic field, including the effects of the electromagnetically induced gravitational perturbation and of the gravitationally induced electromagnetic perturbation, are presented in closed analytic formulas.