Superposition of fields of two Reissner - Nordstrom sources

TL;DR

This paper introduces a five-parameter family of solutions describing the combined gravitational and electromagnetic fields of two Reissner-Nordström sources, detailing a method to solve the Einstein-Maxwell equations for stationary axisymmetric fields.

Contribution

It presents a new five-parameter family of solutions for two Reissner-Nordström sources and details a procedure to solve the associated linear singular integral equations.

Findings

Derived a 5-parametric family of solutions for two charged sources.

Identified equilibrium configurations with specific parameter restrictions.

Provided a detailed solution method for the Einstein-Maxwell equations.

Abstract

In this paper we present a 5-parametric family of static asymptotically flat solutions for the superposed gravitational and electromagnetic fields of two Reissner-Nordstr\"om sources with arbitrary parameters -- masses, charges and separating distance. A procedure for solving of the linear singular integral equation form of the electrovacuum Einstein - Maxwell equations for stationary axisymmetric fields is described in detail. The 4-parametric family of equilibrium configurations of two Reissner-Nordstr\"om sources (one of which should be a black hole and another one -- a naked singularity) presented in our recent paper \cite{Alekseev-Belinski:2007} arises after a restriction of the parameters of the 5-parametric solution presented here by the equilibrium condition which provides the absence in the solution of conical points on the symmetry axis between the sources.