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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• Lectures on Holographic Superfluidity and Superconductivity
• Classical instability of Kerr-AdS black holes and the issue of final state
• Universality class of holographic superconductors
• Vortex lattice for a holographic superconductor
• Characteristic length of an AdS/CFT superconductor
• Superradiance and Instability of Black Holes
• Dynamic critical phenomena in the AdS/CFT duality

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• 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
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• Many phases in a hairy box in three dimensions