Reduction of the effective mass of the Reissner-Nordstrom spacetime

TL;DR

This paper introduces a method to derive the geometrical mass in Reissner-Nordström spacetime, revealing how charge affects the effective mass and comparing it to other mass measures.

Contribution

It presents an inverse method for obtaining electrostatic solutions from vacuum solutions and applies it to analyze the geometrical mass in charged black hole spacetimes.

Findings

Derived the relation M_S^2 = M^2 - Q^2 for the geometrical mass.

Compared geometrical mass with active gravitational mass and mass function.

Provided a new perspective on the effect of charge on effective mass in black hole spacetimes.

Abstract

We derive the Teixeira, Wolk and Som method, for obtaining electrostatic solutions from given vacuum solutions, in its inverse form. Then we use it to obtain the geometrical mass $M_S$ in the Schwarzschild spacetime, and we find $M_S^2=M^2-Q^2$, where $M$ and $Q$ are, respectively, the mass and charge parameters of the Reissner-Nordstr\"om spacetime. We compare $M_S$ to the corresponding active gravitational mass and mass function.