Gravastar-like black hole solutions in $q$-theory

TL;DR

This paper introduces a new class of black hole solutions in $q$-theory, resembling gravastars, with localized energy density outside the horizon, expanding understanding of vacuum structure and black hole mimickers in modified gravity theories.

Contribution

It presents stationary spherically symmetric black hole solutions in $q$-theory with a scalar field, demonstrating gravastar-like configurations with localized energy shells outside the horizon.

Findings

Solutions are asymptotically flat black holes.

Energy density is localized in a thin shell outside the horizon.

Solutions satisfy no-hair theorem conditions due to negative energy regions.

Abstract

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. 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 Black Hole no - hair theorem, thanks to the presence of a region in space in which the energy density is negative.