Novel black holes with scalar hair in the Einstein-Maxwell-Scalar Theory with positive coupling

TL;DR

This paper discovers a new class of stable black hole solutions with scalar hair in Einstein-Maxwell-Scalar theory with positive coupling, expanding understanding of black hole scalarization beyond tachyonic instabilities.

Contribution

It introduces a novel branch of scalar-hairy black holes in EMS theory with positive coupling, differing from known tachyonic scalarization mechanisms.

Findings

Scalar field grows monotonically and approaches a finite constant.

Scalar-hairy solutions deviate with increasing charge but revert to RN solutions at high charge.

Solutions are stable against linearized scalar perturbations.

Abstract

In this work, we find a new branch of hairy black hole solutions in the Einstein-Maxwell-Scalar (EMS) theory in four-dimensional asymptotically flat spacetimes. Different from spontaneous scalarization induced by tachyonic instabilities in Reissner-Nordstr\"{o}m (RN) black holes with a negative coupling parameter, these scalar-hairy black hole solutions arise when the coupling parameter is positive, where nonlinear coupling plays the dominant role, meaning that the coupling is positively correlated with the degree of deviation from the trivial state. Our numerical analysis reveals that the scalar field grows monotonically with the radial coordinate and asymptotically approaches a finite constant, exhibiting behavior that is qualitatively similar to that of the Maxwell potential. In these solutions, an increase in the charge $q$ causes the scalar-hairy solutions to deviate further from the RN state, while excessive charging drives the system back towards hairless solutions. Strengthening the coupling parameter compresses the existence domain of the scalar-hairy state, which lies entirely within the parameter region of RN black holes. Moreover, by evaluating the quasinormal modes, we show that the obtained scalar-hairy solutions are stable against linearized scalar perturbations.