EinsteinMaxwellscalar black holes: The hot, the cold and the bald
Abstract
The phenomenon of spontaneous scalarisation of charged black holes (BHs) has recently motivated studies of various EinsteinMaxwellscalar models. Within these models, different classes of BH solutions are possible, depending on the nonminimal coupling function f (ϕ), between the scalar field and the Maxwell invariant. Here we consider the class wherein both the (bald) electrovacuum ReissnerNordström (RN) BH and new scalarised BHs coexist, and the former are never unstable against scalar perturbations. In particular we examine the model, within this subclass, with a quartic coupling function: f (Φ) = 1 + αΦ^{4}. The domain of existence of the scalarised BHs, for fixed α, is composed of two branches. The first branch (cold scalarised BHs) is continuously connected to the extremal RN BH. The second branch (hot scalarised BHs) connects to the first one at the minimum value of the charge to mass ratio and it includes overcharged BHs. We then assess the perturbative stability of the scalarised solutions, focusing on spherical perturbations. On the one hand, cold scalarised BHs are shown to be unstable by explicitly computing growing modes. The instability is quenched at both endpoints of the first branch. On the other hand, hot scalarised BHs are shown to be stable by using the Sdeformation method. Thus, in the spherical sector this model possesses two stable BH local ground states (RN and hot scalarised). We point out that the branch structure of BHs in this model parallels the one of BHs in five dimensional vacuum gravity, with [MyersPerry BHs, fat rings, thin rings] playing the role of [RN, cold scalarised, hot scalarised] BHs.
 Publication:

Physics Letters B
 Pub Date:
 July 2020
 DOI:
 10.1016/j.physletb.2020.135493
 arXiv:
 arXiv:2002.00963
 Bibcode:
 2020PhLB..80635493B
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 12 pages, 6 figures