Effective gravitational mass of the Ayón-Beato and García metric

In this paper, we calculate the effective gravitational mass of Ayon-Beato and Garcia (AG) regular (nonsingular) 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 values of radial distance, our result gives effective gravitational mass of the Reissner–Nordstrom metric.