Multi-scalar black holes with contingent primary hair: Mechanics and stability

TL;DR

This paper extends magnetically charged black hole solutions to multiple scalar fields, introducing a new type of contingent primary scalar hair, and demonstrates their stability and thermodynamic properties.

Contribution

It generalizes previous single-scalar black hole solutions to multiple scalars, revealing a novel contingent primary hair and analyzing stability and thermodynamics.

Findings

Black holes possess a new type of contingent primary scalar hair.

Solutions are stable to radial perturbations.

Derived thermodynamic relations including a Smarr-type formula.

Abstract

We generalize a class of magnetically charged black holes holes non-minimally coupled to two scalar fields previously found by one of us [gr-qc/9910041] to the case of multiple scalar fields. The black holes possess a novel type of primary scalar hair, which we call a contingent primary hair: although the solutions possess degrees of freedom which are not completely determined by the other charges of the theory, the charges necessarily vanish in the absence of the magnetic monopole. Only one constraint relates the black hole mass to the magnetic charge and scalar charges of the theory. We obtain a Smarr-type thermodynamic relation, and the first law of black hole thermodynamics for the system. We further explicitly show in the two-scalar-field case that, contrary to the case of many other hairy black holes, the black hole solutions are stable to radial perturbations.