Stability of generalized Einstein-Maxwell-scalar 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.

39 pages, 2 figures, journal version, typos corrected, Mathematica notebook

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• Nonsingular black holes and spherically symmetric objects in nonlinear electrodynamics with a scalar field
• Neutral particle collisions near Gibbons-Maeda-Garfinkle-Horowitz-Strominger black holes after shadow observations
• Even-parity stability of hairy black holes in $U(1)$ gauge-invariant scalar-vector-tensor theories
• Hairy black holes in extended Einstein-Maxwell-scalar theories with magnetic charge and kinetic couplings
• Linear instability of hairy black holes in Horndeski theory
• Linear stability of charged warm holes