Asymptotically Anti-de Sitter Spherically Symmetric Hairy Black Holes

Fuente: arXiv
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Main Author: Zheng, Weihao
Format: Preprint
Published: 2024
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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
id 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