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Thermodynamics of Gauss–Bonnet black holes revisited

  • Regular Article - Theoretical Physics
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Abstract

We investigate the Gauss–Bonnet black hole in five dimensional anti-de Sitter spacetimes (GBAdS). We analyze all thermodynamic quantities of the GBAdS, which is characterized by the Gauss–Bonnet coupling c and mass M, comparing with those of the Born–Infeld-AdS (BIAdS), Reissner–Norström-AdS black holes (RNAdS), Schwarzschild-AdS (SAdS), and BTZ black holes. For c<0 we cannot obtain the black hole with positively definite thermodynamic quantities of mass, temperature, and entropy, because the entropy does not satisfy the area law. On the other hand, for c>0, we find the BIAdS-like black hole, showing that the coupling c plays the role of a pseudo-charge. Importantly, we could not obtain the SAdS in the limit of c→0, which means that the GBAdS is basically different from the SAdS. In addition, we clarify the connections between thermodynamic and dynamical stability. Finally, we also conjecture that if a black hole is big and thus globally stable, its quasi-normal modes may take on analytic expressions.

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Authors and Affiliations

  1. Institute of Basic Science and School of Computer Aided Science, Inje University, Gimhae, 621-749, South Korea

    Yun Soo Myung & Yong-Wan Kim

  2. Department of Physics, Sogang University, Seoul, 121-742, South Korea

    Young-Jai Park

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  1. Yun Soo Myung
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  2. Yong-Wan Kim
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Correspondence to Yong-Wan Kim.

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Myung, Y.S., Kim, YW. & Park, YJ. Thermodynamics of Gauss–Bonnet black holes revisited. Eur. Phys. J. C 58, 337–346 (2008). https://doi.org/10.1140/epjc/s10052-008-0745-9

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