Magnetically Charged Euler-Heisenberg Black Holes with Scalar Hair

TL;DR

This paper analytically constructs novel magnetically charged black holes with scalar hair in Einstein-Euler-Heisenberg theory, revealing phase transitions and stability properties influenced by magnetic charge, scalar charge, and matter effects.

Contribution

It provides the first analytical solutions for magnetically charged hairy black holes in Einstein-Euler-Heisenberg theory with detailed thermodynamic analysis.

Findings

Black holes develop three horizons at small Euler-Heisenberg parameter and magnetic charge.

The horizon radius increases with scalar charge and gravitational mass.

A second order phase transition occurs, stabilizing the black hole.

Abstract

We study the Einstein-Euler-Heisenberg theory in the presence of a self interacting scalar field, minimally coupled to gravity. We solve analytically the field equations for the magnetically charged case and we obtain novel magnetically charged hairy black holes. The scalar field dresses the black hole with a secondary scalar hair. The hairy black hole develops three horizons when Euler-Heisenberg parameter and the magnetic charge are small and the horizon radius is getting large when the scalar charge and the gravitational mass are large. The presence of matter and the magnetic field outside the horizon of the black hole increases the temperature only for small black holes. Calculating the heat capacity we show that the asymptotically AdS Euler-Heisenberg hairy black hole undergoes a second order phase transition and then it is stabilized. Also the weak energy condition is violated for the asymptotically AdS Euler-Heisenberg hairy black hole.