Angular and radial stabilities of spontaneously scalarized black holes in the presence of scalar-Gauss-Bonnet couplings
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arXiv
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2024
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| author | Minamitsuji, Masato Mukohyama, Shinji Tsujikawa, Shinji |
| author_facet | Minamitsuji, Masato Mukohyama, Shinji Tsujikawa, Shinji |
| contents | We study the linear stability of spontaneously scalarized black holes (BHs) induced by a scalar field $ϕ$ coupled to a Gauss-Bonnet (GB) invariant $R_{\rm GB}^2$. For the scalar-GB coupling $ξ(ϕ)=(η/8) (ϕ^2+αϕ^4)$, 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 $l \gg 1$. 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 $α\gtrsim -1$, the region in which the scalarized BH is subject to angular Laplacian instabilities can emerge. Provided that $α\lesssim -1$ and $-1/2<αϕ_0^2<-0.1155$, where $ϕ_0$ is the field value on the horizon with a unit of the reduced Planck mass $M_{\rm Pl}=1$, 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 $-βϕ^2 R/16$, 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 $|ϕ_0|=4/\sqrtβ$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_10048 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Angular and radial stabilities of spontaneously scalarized black holes in the presence of scalar-Gauss-Bonnet couplings Minamitsuji, Masato Mukohyama, Shinji Tsujikawa, Shinji General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology High Energy Physics - Theory We study the linear stability of spontaneously scalarized black holes (BHs) induced by a scalar field $ϕ$ coupled to a Gauss-Bonnet (GB) invariant $R_{\rm GB}^2$. For the scalar-GB coupling $ξ(ϕ)=(η/8) (ϕ^2+αϕ^4)$, 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 $l \gg 1$. 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 $α\gtrsim -1$, the region in which the scalarized BH is subject to angular Laplacian instabilities can emerge. Provided that $α\lesssim -1$ and $-1/2<αϕ_0^2<-0.1155$, where $ϕ_0$ is the field value on the horizon with a unit of the reduced Planck mass $M_{\rm Pl}=1$, 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 $-βϕ^2 R/16$, 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 $|ϕ_0|=4/\sqrtβ$, 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. |
| title | Angular and radial stabilities of spontaneously scalarized black holes in the presence of scalar-Gauss-Bonnet couplings |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2403.10048 |