Stability of generalized Einstein-Maxwell-scalar black holes

TL;DR

This paper analyzes the stability of static black holes in generalized Einstein-Maxwell-scalar theories, deriving conditions for stability under different perturbations and applying these to various black hole models, including calculations of quasinormal modes.

Contribution

It provides the first comprehensive stability criteria for black holes in generalized Einstein-Maxwell-scalar theories, including conditions for odd and even parity perturbations and propagation speeds.

Findings

Derived master equations for perturbations.

Established stability conditions that differ from energy conditions.

Calculated quasinormal modes for Einstein-Maxwell-dilaton black holes.

Abstract

We study the stability of static black holes in generalized Einstein-Maxwell-scalar theories. We derive the master equations for the odd and even parity perturbations. The sufficient and necessary conditions for the stability of black holes under odd-parity perturbations are derived. We show that these conditions are usually not similar to energy conditions even in the simplest case of a minimally coupled scalar field. We obtain the necessary conditions for the stability of even-parity perturbations. We also derived the speed of propagation of the five degrees of freedom and obtained the class of theories for which all degrees of freedom propagate at the speed of light. Finally, we have applied our results to various black holes in nonlinear electrodynamics, scalar-tensor theories and Einstein-Maxwell-dilaton theory. For the latter, we have also calculated the quasinormal modes.