On black holes with scalar hairs

TL;DR

This paper constructs exact black hole solutions with scalar hairs using solution-generating methods, showing these hairs originate from scalar potentials and do not correspond to conserved charges, challenging traditional no-hair theorems.

Contribution

The paper introduces a new class of black hole solutions with scalar hairs arising from scalar potentials, which are not associated with symmetries or conserved charges.

Findings

Black holes can have many scalar hairs from the scalar potential.

These hairs are not conserved charges and do not correspond to symmetries.

Black holes remain stable under various perturbations despite scalar hairs.

Abstract

By using the Taylor series method and the solution-generating method, we construct exact black hole solutions with minimally coupled scalar field. We find that the black hole solutions can have many hairs except for the physical mass. These hairs come from the scalar potential. Unlike the mass, there is no symmetry corresponding to these hairs, thus they are not conserved and one cannot understand them as Noether charges. They arise as coupling constants. Although there are many hairs, the black hole has only one horizon. The scalar potential becomes negative for sufficient large $\phi$ (or in the vicinity of black hole singularity). Therefore, the no-scalar-hair theorem does not apply to our solutions since the latter does not obey the dominant energy condition. Although the scalar potential becomes negative for sufficient large $\phi$, the black holes are stable to both odd parity perturbations and scalar perturbations. As for even parity perturbations, we find there remains parameter space for the stability of the black holes. Finally, the black hole thermodynamics are developed.