Scalarization of asymptotically Anti-de Sitter black holes with applications to holographic phase transitions

TL;DR

This paper investigates how certain scalar-tensor gravity models induce scalarization in asymptotically Anti-de Sitter black holes, revealing conditions for phase transitions and implications for dual quantum systems, including liquid-gas transitions.

Contribution

It introduces a novel scalarization mechanism for aAdS black holes via curvature invariants and explores its role in holographic phase transitions, extending understanding of scalar fields in AdS/CFT contexts.

Findings

Scalarization occurs when curvature invariants drop below the BF bound.

Scalarization correlates with a phase transition in the dual quantum system.

Extremal black holes cannot support regular scalar fields on the horizon.

Abstract

We study the spontaneous scalarization of spherically symmetric, static and asymptotically Anti-de Sitter (aAdS) black holes in a scalar-tensor gravity model with non-mininal coupling of the form $\phi^2\left(\alpha{\cal R} + \gamma {\cal G}\right)$, where $\alpha$ and $\gamma$ are constants, while ${\cal R}$ and ${\cal G}$ are the Ricci scalar and Gauss-Bonnet term, respectively. Since these terms act as an effective ``mass'' for the scalar field, non-trivial values of the scalar field in the black hole space-time are possible for {\it a priori} vanishing scalar field mass. In particular, we demonstrate that the scalarization of an aAdS black hole requires the curvature invariant $-\left(\alpha{\cal R} + \gamma {\cal G}\right)$ to drop below the Breitenlohner-Freedman bound close to the black hole horizon, while it asymptotes to a value well above the bound. The dimension of the dual operator on the AdS boundary depends on the parameters $\alpha$ and $\gamma$ and we demonstrate that -- for fixed operator dimension -- the expectation value of this dual operator increases with decreasing temperature of the black hole, i.e. of the dual field theory. When taking backreaction of the space-time into account, we find that the scalarization of the black hole is the dual description of a phase transition in a strongly coupled quantum system, i.e. corresponds to a holographic phase transition. A possible application are liquid-gas quantum phase transitions, e.g. in $^4$He. Finally, we demonstrate that extremal black holes with $AdS_2\times S^2$ near-horizon geometry {\it cannot support regular scalar fields on the horizon} in the scalar-tensor model studied here.