Black hole thermodynamics, conformal couplings, and R^2 terms

TL;DR

This paper investigates the thermodynamics of charged black holes in higher-curvature Lovelock gravity with conformal matter couplings, analyzing their properties, boundary actions, and duality symmetries in both flat and AdS spaces.

Contribution

It provides explicit solutions and boundary actions for black holes in Lovelock theories with matter, including their thermodynamics and duality properties, extending previous analyses to non-minimal matter couplings.

Findings

Charged black holes with regular scalar fields in Lovelock gravity

Explicit boundary actions for well-posed variational problems

Duality symmetry acting on black hole and wave solutions

Abstract

Lovelock theory provides a tractable model of higher-curvature gravity in which several questions can be studied analytically. This is the reason why, in the last years, this theory has become the favorite arena to study the effects of higher-curvature terms in the context of AdS/CFT correspondence. Lovelock theory also admits extensions that permit to accommodate matter coupled to gravity in a non-minimal way. In this setup, problems such as the backreaction of matter on the black hole geometry can also be solved exactly. In this paper, we study the thermodynamics of black holes in theories of gravity of this type, which include both higher-curvature terms, U(1) gauge fields, and conformal couplings with matter fields in D dimensions. These charged black hole solutions exhibit a backreacting scalar field configuration that is regular everywhere outside and on the horizon, and may exist both in asymptotically flat and asymptotically Anti-de Sitter (AdS) spaces. We work out explicitly the boundary action for this theory, which renders the variational problem well-posed and suffices to regularize the Euclidean action in AdS. We also discuss several interrelated properties of the theory, such as its duality symmetry under field redefinition and how it acts on black holes and gravitational wave solutions.