Hairy Lovelock black holes and Stueckelberg mechanism for Weyl symmetry

TL;DR

This paper reviews hairy black hole solutions in Lovelock gravity with conformal scalar coupling, explores their thermodynamics, and discusses a duality transformation revealing constraints from causality bounds in AdS/CFT.

Contribution

It introduces a novel scalar-tensor theory from Lovelock gravity via the Stueckelberg mechanism, revealing a self-duality and analyzing causality bounds in higher dimensions.

Findings

Hairy black holes have regular scalar profiles and AdS asymptotics.

The theory exhibits a self-duality under field redefinition similar to T-duality.

Causality bounds are obeyed at the lower limit but violated at the upper limit, saturating in large D.

Abstract

Lovelock theory of gravity -and, in particular, Einstein theory- admits black hole solutions that can be equipped with a hair by conformally coupling the theory to a real scalar field. This is a secondary hair, meaning that it does not endow the black hole with new quantum numbers. It rather consists of a non-trivial scalar field profile of fixed intensity which turns out to be regular everywhere outside and on the horizon and, provided the cosmological constant is negative, behaves at large distance in a way compatible with the Anti-de Sitter (AdS) asymptotic. In this paper, we review the main features of these hairy black hole solutions, such as their geometrical and thermodynamical properties. The conformal coupling to matter in dimension $D>4$ in principle includes higher-curvature terms. These couplings are obtained from the Lovelock action through the Stueckelberg strategy. As a consequence, the resulting scalar-tensor theory exhibits a self-duality under field redefinition that resembles T-duality. Through this field redefinition, the matter content of the theory transforms into a Lovelock action for a dual geometry. Since the hairy black holes only exist for special relations between the dual Lovelock coupling constants, it is natural to compare those relations with the causality bounds coming from AdS/CFT. We observe that, while the lower causality bound is always obeyed, the upper causality bound is violated. The latter, however, is saturated in the large $D$ limit.