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Entropy of the Dirac Field in Schwarzschild–de Sitter Space-Time via the Membrane Model

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Abstract

There are two event horizons in Schwarzschild–de Sitter space-time, a blackhole horizon and a cosmological horizon. They have different temperatures. Theradiation between them is of course not in thermal equilibrium. According to themembrane model suggested by us, the two horizons can be thought of as twoindependent thermodynamic systems in equilibrium. Their Dirac field entropiesare calculated via a membrane model. The result shows that the entropy of theDirac field is proportional to the sum of the areas of the two event horizons. Ifwe choose the same cutoff as that of Klein–Gordon field, the entropy of theDirac field is \(3\tfrac{1}{2}\) times that of Klein–Gordon field. This agrees with previousresults.

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Authors and Affiliations

  1. National Astronomical Observation, Chinese Academy of Sciences, Beijing, 100012, P.R. China

    Changjun Gao

  2. Shanghi Astronomical Observatory, Chinese Academy of Sciences, Shanghi, 200030, P.R. China

    Changjun Gao

  3. Department of Physics, Beijing Normal University, Beijing, 100875, China

    Wenbiao Liu

Authors
  1. Changjun Gao
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  2. Wenbiao Liu
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Gao, C., Liu, W. Entropy of the Dirac Field in Schwarzschild–de Sitter Space-Time via the Membrane Model. International Journal of Theoretical Physics 39, 2221–2229 (2000). https://doi.org/10.1023/A:1003759914128

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  • DOI: https://doi.org/10.1023/A:1003759914128

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