Angular and radial stabilities of spontaneously scalarized black holes in the presence of scalar-Gauss-Bonnet couplings

Masato Minamitsuji; Shinji Mukohyama; Shinji Tsujikawa

doi:10.1103/PhysRevD.109.104057

paper

Angular and radial stabilities of spontaneously scalarized black holes in the presence of scalar-Gauss-Bonnet couplings

arXiv:2403.10048 · doi:10.1103/PhysRevD.109.104057

Abstract

We study the linear stability of spontaneously scalarized black holes (BHs) induced by a scalar field $ϕ$ coupled to a Gauss-Bonnet (GB) invariant $R_{GB}^{2}$ . For the scalar-GB coupling $ξ (ϕ) = (η /8) (ϕ^{2} + α ϕ^{4})$ , where $η$ and $α$ are constants, we first show that there are no angular Laplacian instabilities of even-parity perturbations far away from the horizon for large multipoles $l ≫ 1$ . The deviation of angular propagation speeds from the speed of light is largest on the horizon, whose property can be used to put constraints on the model parameters. For $α ≳ - 1$ , the region in which the scalarized BH is subject to angular Laplacian instabilities can emerge. Provided that $α ≲ - 1$ and $- 1/2 < α ϕ_{0}^{2} < - 0.1155$ , where $ϕ_{0}$ is the field value on the horizon with a unit of the reduced Planck mass $M_{Pl} = 1$ , there are scalarized BH solutions satisfying all the linear stability conditions throughout the horizon exterior. We also study the stability of spontaneously scalarized BHs in scalar-GB theories with a nonminimal coupling $- β ϕ^{2} R /16$ , where $β$ is a positive constant and $R$ is a Ricci scalar. As the amplitude of the field on the horizon approaches an upper limit $∣ ϕ_{0} ∣ = 4/ β$ , one of the squared angular propagation speeds $c_{Ω -}^{2}$ enters the instability region $c_{Ω -}^{2} < 0$ . So long as $∣ ϕ_{0} ∣$ is smaller than a maximum value determined for each $β$ in the range $β > 5$ , however, the scalarized BHs are linearly stable in both angular and radial directions.

arXiv comment21 pages, 5 figures

Angular and radial stabilities of spontaneously scalarized black holes in the presence of scalar-Gauss-Bonnet couplings

Abstract

References in corpus (73)

Cited by in corpus (4)