Electric force lines of the double Reissner-Nordstrom exact solution

TL;DR

This paper analyzes the electric force lines in a new exact Einstein-Maxwell solution describing two Reissner-Nordstrom sources in equilibrium, highlighting the gravitational and electric field features in various charge configurations.

Contribution

It provides a detailed study of the electric force lines and field features in a novel exact solution involving a naked singularity and a black hole in equilibrium.

Findings

Electric force lines differ significantly with charge sign configurations.

The solution reveals unique field structures near naked singularities and black holes.

Graphical plots illustrate the electric field behavior in various scenarios.

Abstract

Recently, Alekseev and Belinski have presented a new exact solution of the Einstein-Maxwell equations which describes two Reissner-Nordstrom (RN) sources in reciprocal equilibrium (no struts nor strings); one source is a naked singularity, the other is a black hole: this is the only possible configuration for separable object, apart from the well-known extreme case ($m_i=e_i$). In the present paper, after a brief summary of this solution, we study in some detail the coordinate systems used and the main features of the gravitational and electric fields. In particular we graph the plots of the electric force lines in three qualitatively different situations: equal-signed charges, opposite charges and the case of a naked singularity near a neutral black hole.