### Abstract

We investigate dynamical and thermodynamical instability of the 4-d Reissner- Nordström-Anti de-Sitter (RN-AdS) black holes. In accordance with the holographic model of superconductor, we find, by computing the quasi-normal mode, that the RN-AdS black holes are unstable below the critical temperature. We also calculate the difference of the entropy between the RN-AdS black hole and the hairy black hole that emerges below the critical temperature. It is shown that the hairy black hole carries larger entropy than the RN-AdS black hole in the micro-canonical ensemble, which implies that the RN-AdS black holes evolve towards the hairy black holes, due to the instability.

Original language | English |
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Pages | 402-406 |

Number of pages | 5 |

Publication status | Published - 2010 Dec 1 |

Event | 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010 - Kyoto, Japan Duration: 2010 Sep 21 → 2010 Sep 25 |

### Conference

Conference | 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010 |
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Country | Japan |

City | Kyoto |

Period | 10/9/21 → 10/9/25 |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

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## Cite this

*The final fate of instability of Reissner-Nordström-AdS black holes*. 402-406. Paper presented at 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010, Kyoto, Japan.