Mass-Charge Metric in Curved Spacetime

Abstract

In the context of gravitational objects with spherical symmetry, we derive a solution to Einstein’s field equations using two methods leading to the same result. The first is based on a stress-energy tensor that takes into account both the electric field energy of the charge and the gravitational field energy of the mass. The second is based on the mass-energy equivalence and has more general validity. We show that the metric falls within the Weyl class of metrics, representing a static and axisymmetric solution to Einstein’s field equations. The metric, which has a form similar to that of Reisser-Nordström, is used for predictions in strong fields and possibly shows better agreement with observation in high z quasars.