Phase transition for black holes with scalar hair and topological black holes

TL;DR

This paper investigates phase transitions between scalar-haired black holes and topological black holes in anti-de Sitter spaces, revealing a second-order transition in four dimensions and exploring possible decay pathways in three dimensions.

Contribution

It introduces a detailed analysis of phase transitions involving scalar hair and topological black holes, highlighting the order of transitions and decay processes in different dimensions.

Findings

Second-order phase transition between scalar hair black hole and topological black hole in four dimensions.

Possible decay of scalar black hole to non-rotating BTZ black hole in three dimensions.

Identification of free energy differences as key to determining transition order.

Abstract

We study phase transitions between black holes with scalar hair and topological black holes in asymptotically anti-de Sitter spacetimes. As the ground state solutions, we introduce the non-rotating BTZ black hole in three dimensions and topological black hole with hyperbolic horizon in four dimensions. For the temperature matching only, we show that the phase transition between black hole with scalar hair (Martinez-Troncoso-Zanelli black hole) and topological black hole is second-order by using differences between two free energies. However, we do not identify what order of the phase transition between scalar and non-rotating BTZ black holes occurs in three dimensions, although there exists a possible decay of scalar black hole to non-rotating BTZ black hole.