The different phases of hairy black holes in AdS5 space

TL;DR

This paper analyzes the thermodynamics and phase transitions of hairy black holes in AdS5 space, revealing new features like low-temperature black holes and providing analytical solutions for hair formation.

Contribution

It introduces an analytical approach to study fully backreacting hairy black holes in AdS5, highlighting phase transitions and unique thermodynamic properties.

Findings

Existence of phase transitions leading to hairy black holes.

Black holes with arbitrarily low temperature in AdS5.

Analytical solutions for hair formation at critical temperatures.

Abstract

We investigate the thermodynamics of hairy black holes in asymptotically Anti-de Sitter (AdS) space, including backreaction. Resorting to the Euclidean path integral approach, we show that matter conformally coupled to Einstein gravity in five dimensions may exhibit a phase transition whose endpoint turns out to be a hairy black hole in AdS5 space. The scalar field configuration happens to be regular everywhere outside and on the horizon, and behaves asymptotically in such a way that respects the AdS boundary conditions that are relevant for AdS/CFT. The theory presents other peculiar features in the ultraviolet, like the existence of black holes with arbitrarily low temperature in AdS5. This provides a simple setup in which the fully backreacting problem of a hair forming in AdS at certain critical temperature can be solved analytically.