Reissner–Nordstrom metric in unimodular theory of gravity

Abstract

We study the modified Reissner–Nordstrom (RN) metric in the unimodular gravity. So far the spherical symmetric Einstein field equation in unimodular gravity has been studied in the absence of any source. We consider static electric and magnetic charge as source. We solve for Maxwell equations in unimodular gravitational background. We show that in unimodular gravity, the electromagnetic field strength tensor is modified. We also show that the solution in unimodular gravity differs from the usual RN metric in Einstein gravity with some corrections. We further study the thermodynamical properties of the RN black hole solution in this theory.