### 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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Title of host publication | Proceedings of the 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010 |

Pages | 402-406 |

Number of pages | 5 |

Publication status | Published - 2010 |

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

### Other

Other | 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010 |
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City | Kyoto |

Period | 10/9/21 → 10/9/25 |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Proceedings of the 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010*(pp. 402-406)

**The final fate of instability of Reissner-Nordström-AdS black holes.** / Koga, Jun Ichirou; Maeda, Kengo; Fujii, Shunsuke.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010.*pp. 402-406, 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010, Kyoto, 10/9/21.

}

TY - GEN

T1 - The final fate of instability of Reissner-Nordström-AdS black holes

AU - Koga, Jun Ichirou

AU - Maeda, Kengo

AU - Fujii, Shunsuke

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84887488572&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887488572&partnerID=8YFLogxK

M3 - Conference contribution

SP - 402

EP - 406

BT - Proceedings of the 20th Workshop on General Relativity and Gravitation in Japan, JGRG 2010

ER -