The shadow and quasinormal modes of the asymptotically flat hairy black holes with a dilaton potential
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| Format: | Preprint |
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2025
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| author | Xiong, Sheng-Han Li, Yong-Zhuang Kuang, Xiao-Mei Matyjasek, Jerzy |
| author_facet | Xiong, Sheng-Han Li, Yong-Zhuang Kuang, Xiao-Mei Matyjasek, Jerzy |
| contents | In this article, the shadow and the quasinormal modes (QNMs) of an exact asymptotically flat hairy electrically charged black hole solution with a dilaton potential are investigated. Using the {constraint} equation among the integration constant $η$ of the gravitational field, the mass $M$, the electric charge $Q$ and the coupling constant $ν$ between the $U(1)$ field and the dilaton field, we find that the shadow radii, the Lyapunov exponent $λ$ and the coordinate angular velocity $Ω_{c}$ only significantly affected by $ν$ if the $Q$ is close to the extremal value, especially when $ν$ approaches to one. Furthermore, the QNMs are numerically computed by using the Hatsuda method and verify with the higher-order WKB approximations with the Padé summation. We find that the QNMs are close to that of the low energy limit of the string theory when $ν$ is large enough. In the eikonal limit, the real and imaginary parts are proved to be given by $Ω_{c}$ and $λ$, respectively. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_03270 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The shadow and quasinormal modes of the asymptotically flat hairy black holes with a dilaton potential Xiong, Sheng-Han Li, Yong-Zhuang Kuang, Xiao-Mei Matyjasek, Jerzy General Relativity and Quantum Cosmology In this article, the shadow and the quasinormal modes (QNMs) of an exact asymptotically flat hairy electrically charged black hole solution with a dilaton potential are investigated. Using the {constraint} equation among the integration constant $η$ of the gravitational field, the mass $M$, the electric charge $Q$ and the coupling constant $ν$ between the $U(1)$ field and the dilaton field, we find that the shadow radii, the Lyapunov exponent $λ$ and the coordinate angular velocity $Ω_{c}$ only significantly affected by $ν$ if the $Q$ is close to the extremal value, especially when $ν$ approaches to one. Furthermore, the QNMs are numerically computed by using the Hatsuda method and verify with the higher-order WKB approximations with the Padé summation. We find that the QNMs are close to that of the low energy limit of the string theory when $ν$ is large enough. In the eikonal limit, the real and imaginary parts are proved to be given by $Ω_{c}$ and $λ$, respectively. |
| title | The shadow and quasinormal modes of the asymptotically flat hairy black holes with a dilaton potential |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2508.03270 |