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Effective gravitational mass of the Ayón-Beato and García metric. (English) Zbl 1320.83028

Summary: In this paper, we calculate the effective gravitational mass of Ayón-Beato and García (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-Nordström metric.

MSC:

83C22 Einstein-Maxwell equations
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
83C57 Black holes
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