  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.
