Four-dimensional black holes with scalar hair in nonlinear electrodynamics

TL;DR

This paper presents new four-dimensional charged black hole solutions with scalar hair in nonlinear electrodynamics, analyzing their thermodynamics and phase transitions at different temperatures.

Contribution

It introduces analytical and numerical solutions for charged hairy black holes in nonlinear electrodynamics, exploring their thermodynamic behavior and phase transitions.

Findings

Scalar hair affects black hole thermodynamics.

Phase transitions occur at a fixed critical temperature.

Scalar hair is thermodynamically favored at low temperatures.

Abstract

We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and a U(1) nonlinear electromagnetic field. Solving analytically and numerically the coupled system for both power-law and Born-Infeld type electrodynamics, we find charged hairy black hole solutions. Then, we study the thermodynamics of these solutions and we find that at a low temperature the topological charged black hole with scalar hair is thermodynamically preferred, whereas the topological charged black hole without scalar hair is thermodynamically preferred at a high temperature for power-law electrodynamics. Interestingly enough, these phase transitions occur at a fixed critical temperature and do not depend on the exponent $p$ of the nonlinearity electrodynamics.