Asymptotically Anti-de Sitter Spherically Symmetric Hairy Black Holes
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918504699002880 |
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| author | Zheng, Weihao |
| author_facet | Zheng, Weihao |
| contents | We construct one-parameter families of static spherically symmetric asymptotically anti-de Sitter black hole solutions $(\mathcal{M},g_ε,ϕ_ε)$ to the Einstein-Maxwell-(charged) Klein-Gordon equations. Each family bifurcates off a sub-extremal Reissner-Nordström-AdS spacetime $(\mathcal{M},g_{0},ϕ_{0}\equiv0)$. For a co-dimensional one set of black hole parameters, we show that Dirichlet (respectively Neumann) boundary conditions can be imposed for the scalar field. The construction provides a counter-example to a version of the no-hair conjecture in the context of a negative cosmological constant. Our result is based on our companion work [W. Zheng, \emph{Exponentially-growing Mode Instability on the Reissner-Nordström-Anti-de-Sitter black holes}], in which the existence of linear hair and growing mode solutions have been established. In the charged scalar field case, our result provides the first rigorous mathematical construction of the so-called holographic superconductors, which are of particular significance in high-energy physics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_04758 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotically Anti-de Sitter Spherically Symmetric Hairy Black Holes Zheng, Weihao General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs We construct one-parameter families of static spherically symmetric asymptotically anti-de Sitter black hole solutions $(\mathcal{M},g_ε,ϕ_ε)$ to the Einstein-Maxwell-(charged) Klein-Gordon equations. Each family bifurcates off a sub-extremal Reissner-Nordström-AdS spacetime $(\mathcal{M},g_{0},ϕ_{0}\equiv0)$. For a co-dimensional one set of black hole parameters, we show that Dirichlet (respectively Neumann) boundary conditions can be imposed for the scalar field. The construction provides a counter-example to a version of the no-hair conjecture in the context of a negative cosmological constant. Our result is based on our companion work [W. Zheng, \emph{Exponentially-growing Mode Instability on the Reissner-Nordström-Anti-de-Sitter black holes}], in which the existence of linear hair and growing mode solutions have been established. In the charged scalar field case, our result provides the first rigorous mathematical construction of the so-called holographic superconductors, which are of particular significance in high-energy physics. |
| title | Asymptotically Anti-de Sitter Spherically Symmetric Hairy Black Holes |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2410.04758 |