Thermodynamics of black holes with conformal scalar hair

ANDRES GOYA

Santiago

Conferencia; Gravity at UCEN 2019: Recent developments in Black Hole Physics and Cosmology; 2019

Universidad Central de Chile

Lovelock theory provides a tractable higher-dimensional model where many problems can be addressed analytically. For example, it allows to study the effect of higher curvature terms in the context of holography. Interestingly, it is possible to extend Lovelock gravity to a conformally invariant version of it by introducing couplings to a scalar field in a non-minimal way. The equations of motion of these Lovelock-like theories are still second order in both the metric and the scalar field. Such scalar-tensor theories support hairy black hole solutions in arbitrary dimensions, thus evading existing no-go theorems for D>4. Remarkably, it is possible to study their thermodynamics analytically taking into account the backreaction of the scalar field. In this talk we will focus on the five dimensional case with AdS asymptotics and study the thermodynamics of hairy black holes with and without electric charge. We will find that they exhibit a Hawking-Page phase transition where the hairy black hole is the preferable configuration above a certain critical temperature. In order to do that we will need to build the appropriate boundary terms to evaluate the on-shell action to obtain the Helmholtz free energy and compare its value for each geometry of interest.