Electrostatics in a Schwarzschild black hole pierced by a cosmic string

TL;DR

This paper derives the electrostatic potential and self-energy of a point charge near a Schwarzschild black hole with a cosmic string, and discusses implications for black hole entropy bounds.

Contribution

It provides explicit formulas for electrostatics in this spacetime and links the results to black hole thermodynamics, extending previous analyses.

Findings

Explicit electrostatic potential expression derived.

Electrostatic self-energy calculated.

Upper entropy bound for charged objects confirmed.

Abstract

We explicitly determine the expression of the electrostatic potential generated by a point charge at rest in the Schwarzschild black hole pierced by a cosmic string. We can then calculate the electrostatic self-energy. From this, we find again the upper entropy bound for a charged object by employing thermodynamics of the black hole.