Topological black holes in pure Gauss-Bonnet gravity and phase transitions

TL;DR

This paper investigates topological black holes in pure Gauss-Bonnet gravity, analyzing their thermodynamics and phase transitions in a dual quantum field theory, revealing conditions for scalar hair formation and the nature of phase transitions.

Contribution

It introduces the study of charged topological black holes in pure Gauss-Bonnet gravity and explores their phase transitions and scalar hair development in the dual field theory.

Findings

Black holes can develop scalar hair below a critical temperature.

Phase transitions can be first or second order depending on scalar coupling.

Hairy black hole states are energetically favored over non-hairy solutions.

Abstract

We study charged, static, topological black holes in pure Gauss-Bonnet gravity in asymptotically AdS space. As in general relativity, the theory possesses a unique nondegenerate AdS vacuum. It also admits charged black hole solutions which asymptotically behave as the Reissner-Nordstr\"{o}m AdS black hole. We discuss black hole thermodynamics of these black holes. Then we study phase transitions in a dual quantum field theory in four dimensions, with the St\"{u}ckelberg scalar field as an order parameter. We find in the probe limit that the black hole can develop hair below some critical temperature, which suggests a phase transition. Depending on the scalar coupling constants, the phase transition can be first or second order. Analysis of the free energy reveals that, comparing the two solutions, the hairy state is energetically favorable, thus a phase transition will occur in a dual field theory.