Einstein-Maxwell-scalar black holes: the hot, the cold and the bald

Understand

The phenomenon of spontaneous scalarisation of charged black holes (BHs) has recently motivated studies of various Einstein-Maxwell-scalar models.

• Within these models, different classes of BH solutions are possible, depending on the non-minimal coupling function $f(\phi)$, between the scalar field and the Maxwell invariant.
• Here we consider the class wherein both the (bald) electrovacuum Reissner-Nordstr\"om (RN) BH and new scalarised BHs co-exist, and the former are never unstable against scalar perturbations.
• In particular we examine the model, within this subclass, with a quartic coupling function: $f(\Phi) = 1+\alpha \Phi ^4$.