Hairy Black Holes in Disformal Scalar-Tensor Gravity Theories

TL;DR

This paper demonstrates that scalar-tensor theories with disformal couplings can admit hairy black hole solutions with diverse asymptotics and topologies, revealing complex thermodynamic phase behavior including phase transitions and a triple point.

Contribution

It shows that the no-hair theorem can be evaded in disformal scalar-tensor theories, introducing new black hole solutions with rich thermodynamics and phase structures.

Findings

Hairy black holes with various asymptotics and topologies are possible.

Disformal factors influence thermodynamic stability and phase transitions.

Existence of a triple point where three phases coexist.

Abstract

We show that the no-hair theorem for scalar-tensor theories with bi-metric structure can be evaded. We find that hairy black hole solutions in the presence of an electric charge admit AdS, flat or dS asymptotics with spherical, flat, or hyperbolic base manifolds. Spherically symmetric, asymptotically flat black holes and asymptotically AdS configurations with any horizon topology are compatible with a regular scalar field on and outside the event horizon. The latter presents a rich thermodynamic behavior induced by the disformal factor that enters as a coupling parameter in the theory. In the grand canonical ensemble, there is an interplay of stability and first-order phase transitions between thermal AdS, the hairy black hole, and the Reissner-Nordstr\"om-AdS black hole, whose thermodynamic phase space resembles a solid-liquid-gas system, with an electric potential playing the role of pressure. In close analogy, there is a triple point where the three phases coexist, being equally probable.