Spherically Symmetric Configurations in Unimodular Gravity

Unimodular gravity (UG) is considered, under many aspects, equivalent to General Relativity (GR), even if the theory is invariant under a more restricted diffeomorphic class of transformations. We discuss the conditions for the equivalence between the two formulations by applying the UG to the static and spherically symmetric configurations being the energy-momentum tensor sourced by a scalar field or by the electromagnetic field. We argue that the equivalence between UG and GR may be broken when analyzing the stability of the solutions at perturbative level.