Effective gravitational mass of the Ay\'{o}n-Beato and Garc\'{\i}a metric

TL;DR

This paper calculates the effective gravitational mass of a regular, non-singular black hole solution, revealing its dependence on charge and distance, and comparing it to the Reissner-Nordström metric at large distances.

Contribution

It provides a detailed calculation of the effective gravitational mass for the Ayón-Beato and García metric, highlighting its dependence on charge and radial distance, and its relation to known solutions.

Findings

Effective gravitational mass varies with charge-to-mass ratio.

Mass can be negative, zero, or positive depending on parameters.

At large distances, the mass matches that of Reissner-Nordström.

Abstract

In this paper, we calculate the effective gravitational mass of Ay\'{o}n-Beato and Garc\'{\i}a regular (non-singular) static spherically symmetric asymptotically Minkowskian metric that is a solution to Einstein's equations coupled with a nonlinear electromagnetic field. The effective gravitational mass is negative, zero, or positive that depends on the ratio of magnitude of electric charge to the ADM mass and the ratio of the radial distance to the ADM mass. As expected, at large value of radial distance, our result gives effective gravitational mass of the Reissner-Nordstr\"om metric.