Reissner Nordstrom Metric in Unimodular Theory of Gravity

TL;DR

This paper explores the modified Reissner Nordstrom black hole solution within unimodular gravity, revealing differences from Einstein gravity and analyzing the thermodynamics of these black holes.

Contribution

It introduces a modified Reissner Nordstrom metric in unimodular gravity, including electromagnetic field modifications and thermodynamical analysis, which are novel compared to prior Einstein gravity studies.

Findings

Electromagnetic field strength tensor is modified in unimodular gravity.

The black hole solution differs from the standard Reissner Nordstrom metric with specific corrections.

Thermodynamical properties of the black hole are analyzed within this modified framework.

Abstract

We study the modified Reissner Nordstrom 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 R-N metric in Einstein gravity with some corrections. We further study the thermodynamical properties of the R-N black-hole solution in this theory.