On naked singularities in the extreme double Reissner-Nordstr\"{o}m solution

TL;DR

This paper analytically investigates the conditions under which naked singularities appear in binary systems, specifically in the double Reissner-Nordström solution, highlighting the role of negative masses in singular surface formation.

Contribution

It provides a simple analytical framework to determine when naked singularities occur in the double Reissner-Nordström solution, emphasizing the impact of negative masses.

Findings

Naked singularities are linked to negative masses in the solution.

Singular surfaces can be avoided by ensuring positive mass conditions.

The study clarifies conditions for singularity development off the axis.

Abstract

We present a quite simple analytical study on the appearance or absence of naked singularities in binary systems. As an example we consider the double Reissner-Nordstr\"om solution and fix the conditions it should satisfy in order to avoid or develop singular surfaces off the axis. The proof shows that singular surfaces appear as a consequence of the presence of negative masses in the solution.