Linear perturbations of dyonic black holes in the lowest-order $U(1)$ gauge-invariant scalar-vector-tensor theories
Kitaro Taniguchi, Shunta Nishimura, Naoki Tsukamoto, Ryotaro Kase
TL;DR
The paper develops a comprehensive framework to study linear perturbations of dyonic black holes in the lowest-order U(1) gauge-invariant SVT theories, where magnetic charge induces mixing between odd- and even-parity sectors. It derives the second-order perturbation action, identifies the dynamical DOFs, and establishes explicit ghost and Laplacian stability conditions for all multipoles, including l≥2, l=1, and l=0. The authors then apply the framework to extended Einstein-Maxwell-scalar models, obtaining concrete viability criteria for various couplings (g1, g2, g3) and showing, for example, stability of GMGHS-type solutions with electric and magnetic charges and general stability of axionic couplings. This work provides a robust tool for testing hairy dyonic BH solutions and sets the stage for future quasinormal-mode analyses and explorations of nonlinear electrodynamics.
Abstract
We study linear perturbations on top of the static and spherically symmetric background of dyonic black hole solutions endowed with electric and magnetic charges, as well as a scalar hair, in the lowest-order $U(1)$ gauge-invariant scalar-vector-tensor theories. The presence of magnetic charges in the background solutions gives rise to a mixing between the odd-parity and even-parity sectors of perturbations, which makes it impossible to analyze each sector separately. Thus, we expand the action up to second order in both odd-parity and even-parity perturbations and derive the general conditions for the absence of ghosts and Laplacian instabilities. We apply these general conditions to extended Einstein-Maxwell-scalar theories, which encompass numerous types of concrete models from the literature known to have dyonic black hole solutions with the scalar hair, and examine their stabilities. Our general framework for studying stability conditions and dynamics of perturbations can be applied to a wide variety of theories, including nonlinear electrodynamics coupled to a scalar field, as well as to calculations of black hole quasinormal modes.