Scalar hairy black holes in Einstein-Maxwell-conformally coupled scalar theory

TL;DR

This paper explores scalar hairy black holes within Einstein-Maxwell-conformally coupled scalar theory, revealing new scalarized solutions and analyzing their stability and properties across different coupling parameters.

Contribution

It introduces new scalar hairy black hole solutions in EMCS theory with varying coupling parameter and analyzes their stability and scalarization behavior.

Findings

Unstable Reissner-Nordström black holes lead to infinite branches of scalarized black holes.

For positive coupling, a single branch of scalarized solutions is developed.

Numerical solutions for charged BBMB black holes are obtained at zero coupling.

Abstract

We obtain scalar hairy black holes from Einstein-Maxwell-conformally coupled scalar (EMCS) theory with the scalar coupling parameter $\alpha$ to the Maxwell term. In case of $\alpha=0$, the $\alpha=0$ EMCS theory provides constant (charged) scalar hairy black hole and charged BBMB (Bocharova-Bronnikov-Melnikov-Bekenstein) black hole where the former is stable against full perturbations, while the latter remains unstable because it belongs to an extremal black hole. It is noted that for $\alpha\not=0$, the unstable Reissner-Nordstr\"{o}m black holes without scalar hair imply infinite branches of $n=0(\alpha \ge 8.019),1(\alpha \ge 40.84),2(\alpha \ge 99.89),\cdots$ scalarized charged black holes. In addition, for $\alpha>0$, we develop a single branch of scalarized charged black hole solutions inspired by the constant scalar hairy black hole. Finally, we obtain the numerical charged BBMB black hole solution from the $\alpha=0$ EMCS theory.