Spherically Symmetric Configurations in Unimodular Gravity

Abstract

Unimodular gravity (UG) is often deemed comparable to General Relativity (GR) in many respects, despite the theory exhibiting invariance under a more limited set of diffeomorphic transformations. The discussion we propose in this work relies on the criteria for establishing the equivalence between these two formulations, specifically exploring UG’s application to static and spherically symmetric configurations with the energy-momentum tensor originating from either a scalar field or an electromagnetic field. We find that the equivalence between UG and GR might be disrupted when scrutinizing the stability of solutions at a perturbative level.