Eur. Phys. J. C (2016) 76: 677
https://doi.org/10.1140/epjc/s10052-016-4526-6

Regular Article - Theoretical Physics

Four-dimensional black holes with scalar hair in nonlinear electrodynamics

¹ Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción, Chile
² Departamento de Enseñanza de las Ciencias Básicas, Universidad Católica del Norte, Larrondo 1281, Coquimbo, Chile
³ Facultad de Ingeniería, Universidad Diego Portales, Avenida Ejército Libertador 441, Casilla 298-V, Santiago, Chile
⁴ Departamento de Física y Astronomía, Facultad de Ciencias, Universidad de La Serena, Avenida Cisternas 1200, La Serena, Chile

^* e-mail: pablo.gonzalez@udp.cl

Received: 14 June 2016
Accepted: 21 November 2016
Published online: 7 December 2016

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 nonlinear electrodynamics.