Gravastar-like black hole solutions in q-theory

We present a stationary spherically symmetric solution of the Einstein equations, with a source generated by a scalar field of q-theory. In this theory Riemannian gravity, as described by the Einstein-Hilbert action, is coupled to a three-form field that describes the dynamical vacuum. Formally it behaves like a matter field with its own stress-energy tensor, equivalent to a scalar field minimally coupled to gravity. The asymptotically flat solutions obtained to the field equations represent black holes (BHs). For a sufficiently large horizon radius the energy density is localized within a thin spherical shell situated just outside of the horizon, analogous to a gravastar. The resulting solutions to the field equations, which admit this class of configurations, satisfy existence conditions that stem from the BH no-hair theorem, thanks to the presence of a region in space in which the energy density is negative.