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Higher order WKB corrections to black hole entropy in brick wall formalism

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Abstract

We calculate the statistical entropy of a quantum field with an arbitrary spin propagating on the spherical symmetric black hole background by using the brick wall formalism at higher orders in the WKB approximation. For general spins, we find that the correction to the standard Bekenstein–Hawking entropy depends logarithmically on the area of the horizon. Furthermore, we apply this analysis to the Schwarzschild and Schwarzschild–AdS(dS) black holes and discuss our results.

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Notes

  1. Throughout the paper we shall work with the signature (−,+,+,+), and c=G=k B =1.

  2. For a given value of spin |p|, there are 2p+1 equivalent spin states. (E.g. for fermions we have |p|=1/2 and p=1/2,−1/2.)

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Acknowledgements

We would like to thank E. Son and M. Eune for discussions. S. Kulkarni wish to thank L. Sriramkumar and S.K. Modak for their useful comments and suggestions. S. Kulkarni is being supported by National Research Foundation (NRF) grant funded by the Korea government (MEST) through the Center for Quantum Spacetime (CQUeST) of Sogang University with grant number 2005-0049409. W. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0008359).

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  1. Center for Quantum Spacetime (CQUeST), Sogang University, Seoul, 121-742, South Korea

    Wontae Kim & Shailesh Kulkarni

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

    Wontae Kim

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  1. Wontae Kim
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Correspondence to Shailesh Kulkarni.

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Kim, W., Kulkarni, S. Higher order WKB corrections to black hole entropy in brick wall formalism. Eur. Phys. J. C 73, 2398 (2013). https://doi.org/10.1140/epjc/s10052-013-2398-6

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