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Note on generalized gravitational entropy in Lovelock gravity

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Abstract

The recently proposed gravitational entropy generalize the usual black hole entropy to Euclidean solutions without U(1) symmetry in the framework of Einstein gravity. The entropy of such smooth configuration is given by the area of minimal surface, therefore explaining the Ryu-Takayanagi formula of holographic entanglement entropy. In this note we investigate the generalized gravitational entropy for general Lovelock gravity in arbitrary dimensions. We use the replica trick and consider the Euclidean bulk spacetime with conical singularity localized at a codimension two surface. We obtain a constraint equation for the surface by requiring the bulk equation of motion to be of good behavior. When the bulk spacetime is maximally symmetric, the constraints show that the traces of the extrinsic curvatures of the surface are vanishing, i.e. the surface has to be geometrically a minimal surface. However the constraint equation cannot be obtained by the variation of the known functional for holographic entanglement entropy in Lovelock gravity.

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Authors and Affiliations

  1. Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, No. 5 Yiheyuan Road, Beijing, 100871, P. R. China

    Bin Chen & Jia-ju Zhang

  2. Center for High Energy Physics, Peking University, No. 5 Yiheyuan Road, Beijing, 100871, P. R. China

    Bin Chen

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  1. Bin Chen
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  2. Jia-ju Zhang
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Correspondence to Jia-ju Zhang.

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ArXiv ePrint: 1305.6767

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Chen, B., Zhang, Jj. Note on generalized gravitational entropy in Lovelock gravity. J. High Energ. Phys. 2013, 185 (2013). https://doi.org/10.1007/JHEP07(2013)185

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  • DOI: https://doi.org/10.1007/JHEP07(2013)185

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