Charged scalar-tensor solitons and black holes with (approximate) Anti-de Sitter asymptotics

TL;DR

This paper explores charged scalar-tensor black holes with approximate Anti-de Sitter asymptotics, revealing stability properties and limitations on scalar soliton charge inclusion due to electric divergence issues.

Contribution

It demonstrates the existence of charged black holes with scalar hair in a shift-symmetric scalar-tensor model and analyzes their thermodynamic stability and asymptotic behavior.

Findings

Black holes with scalar hair exist only above extremal RNAdS horizon radius.

A divergence of electric monopole prevents charged scalar soliton generalization.

Large black holes exhibit a stable phase, small ones do not.

Abstract

We discuss charged and static solutions in a shift-symmetric scalar-tensor gravity model including a negative cosmological constant. The solutions are only approximately Anti-de Sitter (AdS) asymptotically. While spherically symmetric black holes with scalar-tensor hair do exist in our model, the uncharged spherically symmetric scalar-tensor solitons constructed recently cannot be generalised to include charge. We point out that this is due to the divergence of the electric monopole at the origin of the coordinate system, while higher order multipoles are well-behaved. We also demonstrate that black holes with scalar hair exist only for horizon value larger than that of the corresponding {\it extremal} Reissner-Nordstr\"om-AdS (RNAdS) solution, i.e. that we cannot construct solutions with arbitrarily small horizon radius. We demonstrate that for fixed $Q$ a horizon radius exists at which the specific heat $C_Q$ diverges - signalling a transition from thermodynamically unstable to stable black holes. In contrast to the RNAdS case, however, we have only been able to construct a stable phase of large horizon black holes, while a stable phase of small horizon black holes does not (seem to) exist.