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Entropy quantization of Reissner-Nordström de Sitter black hole via adiabatic covariant action

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Abstract

Based on the ideas of adiabatic invariant quantity, we attempt to quantize the entropy of a charged black hole in de Sitter spacetime in two different coordinates. The entropy spectrum is obtained by imposing Bohr-Sommerfeld quantization rule and the laws of black hole thermodynamics to the modified adiabatic covariant action of the charged black hole. The result shows that the spacing of entropy spectrum is equidistant, and the corresponding horizon area quantum is identical to Bekenstein’s result. Interestingly, in contrast to the quasinormal mode analysis, we note that there is no need to impose the small charge limit for the obtained entropy spectrum of the charged black hole. We also note that the modified adiabatic covariant action gives the same value for the black hole entropy spectrum in different coordinate frames. This is a physically desired result since the entropy spectrum should be invariant under the coordinate transformations.

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Acknowledgments

This work is supported in part by the Scientific Research Foundation of the Education Department of Liaoning Province, China (Grant No. L2011195).

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Authors and Affiliations

  1. College of Physics Science and Technology, Shenyang Normal University, Shenyang, 110034, China

    Hui-Ling Li, Rong Lin & Li-Ying Cheng

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  1. Hui-Ling Li
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  2. Rong Lin
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  3. Li-Ying Cheng
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Correspondence to Hui-Ling Li.

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Li, HL., Lin, R. & Cheng, LY. Entropy quantization of Reissner-Nordström de Sitter black hole via adiabatic covariant action. Gen Relativ Gravit 45, 865–875 (2013). https://doi.org/10.1007/s10714-013-1510-4

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  • DOI: https://doi.org/10.1007/s10714-013-1510-4

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