The final fate of instability of Reissner-Nordström-anti-de Sitter black holes by charged complex scalar fields

Abstract

We investigate instability of 4-dimensional Reissner-Nordström-anti-de Sitter (RN-AdS${}_4$) black holes with various topologies by charged scalar field perturbations. We numerically find that the RN-AdS${}_4$ black holes become unstable against the linear perturbations below a critical temperature. It is analytically shown that charge extraction from the black holes occurs during the unstable evolution. To explore the end state of the instability, we perturbatively construct static black hole solutions with the scalar hair near the critical temperature. It is numerically found that the entropy of the hairly black hole is always larger than the one of the unstable RN-AdS${}_4$ black hole in the microcanonical ensemble. Our results support the speculation that the black hole with charged scalar hair always appears as the final fate of the instability of the RN-AdS${}_4$ black hole.

9 pages, 4 figures. To appear in PRD

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• Non-equilibrium Condensation Process in a Holographic Superconductor
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• Quasinormal modes of a massless charged scalar field on a small Reissner-Nordström-anti-de Sitter black hole
• Superradiant instability of charged massive scalar field in Kerr-Newman-anti-de Sitter black hole
• Phase transitions and regions of stability in Reissner-Nordström holographic superconductors
• Excited hairy black holes: dynamical construction and level transitions
• Descalarization by Quenching Charged Hairy Black Hole in asymptotically AdS spacetime
• Stability of small charged anti-de Sitter black holes in the Robin boundary
• Stability of Holographic Superconductors
• Holographic superconductor in the exact hairy black hole
• Hairy black holes in AdS with Robin boundary conditions
• Vortex flow for a holographic superconductor
• Holographic thermal correlators from recursions
• Many phases in a hairy box in three dimensions