AdS Monopole Black Hole and Phase Transition

TL;DR

This paper investigates monopole black hole solutions in an Einstein-SO(3) Yang-Mills-Higgs system with negative cosmological constant, analyzing phase transitions and stability depending on system parameters.

Contribution

It introduces new monopole black hole solutions and characterizes their phase transitions, including first and second order, based on cosmological constant and Higgs field parameters.

Findings

Identified critical values of the cosmological constant for phase transitions.

Found conditions for first and second order phase transitions.

Described thermodynamical stability and properties of monopole black holes.

Abstract

We study the Einstein-SO(3)Yang-Mills-Higgs system with a negative cosmological constant, and find the monopole black hole solutions as well as the trivial Reissner-Nordstr\"{o}m black hole. We discuss thermodynamical stability of the monopole black hole in an isolated system. We expect a phase transition between those two black holes when the mass of a black hole increases or decreases. The type of phase transition depends on the cosmological constant $\Lambda$ as well as the vacuum expectation value $v$ and the coupling constant $\lambda$ of the Higgs field. Fixing $\lambda$ small, we find there are two critical values of the cosmological constant $\Lambda_{\rm cr (1)}(v)$ and $\Lambda_{\rm cr(2)}(v)$, which depend on $v$. If $\Lambda_{\rm cr(1)}(v)<\Lambda (<0)$, we find the first order transition, while if $\Lambda_{\rm cr(2)}(v)<\Lambda<\Lambda_{\rm cr(1)}(v)$, the transition becomes second order. For the case of $\Lambda_{b}(v)<\Lambda<\Lambda_{\rm (2)}(v)$, we again find the first order irreversible transition from the monopole black hole to the extreme Reissner-Nordstr\"{o}m black hole. Beyond $\Lambda_{b}(v)$, no monopole black hole exists. We also discuss thermodynamical properties of the monopole black hole in a thermal bath system.