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Casimir Energy for Spherical Shell in Schwarzschild Black Hole Background

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Abstract

In this paper, we consider the Casimir energy of massless scalar fields which satisfy the Dirichlet boundary condition on a spherical shell. Outside the shell, the spacetime is assumed to be described by the Schwarzschild metric, while inside the shell it is taken to be the flat Minkowski space. Using zeta function regularization and heat kernel coefficients we isolate the divergent contributions of the Casimir energy inside and outside the shell, then using the renormalization procedure of the bag model the divergent parts are cancelled, finally obtaining a renormalized expression for the total Casimir energy.

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Authors and Affiliations

  1. Physics Dept, Inst. for Studies in Theor. Physics and Mathematics (IPM), P. O. Box 19395-5531, Tehran, Iran

    M. R. Setare

  2. Department of Physics, Sharif University of Technology, Tehran, Iran

    M. R. Setare

  3. Department of Physics, Yarmouk University, Irbid-, Jordan

    M. B. Altaie

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  1. M. R. Setare
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  2. M. B. Altaie
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Correspondence to M. R. Setare.

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Setare, M.R., Altaie, M.B. Casimir Energy for Spherical Shell in Schwarzschild Black Hole Background. General Relativity and Gravitation 36, 331–341 (2004). https://doi.org/10.1023/B:GERG.0000010479.98616.da

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