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An Inhomogeneous Jacobi equation for minimal surfaces and perturbative change of Holographic Entanglement Entropy. (arXiv:1710.02088v2 [hep-th] CROSS LISTED)
来源于:arXiv
The change in Holographic entanglement entropy (HEE) for small fluctuations
about pure anti De Sitter (AdS) is obtained by a perturbative expansion of the
area functional in terms of the change in the bulk metric and the embedded
extremal surface. However, it is known that change in the embedding appears in
second order or higher. It was shown that these changes in the embedding can be
calculated in the $2+1$ dimensional case by solving a generalized geodesic
deviation equation. We generalize this result to arbitrary dimensions by
deriving an inhomogeneous form of the Jacobi equation for minimal surfaces. The
solutions of this equation map a minimal surface in a given space time to a
minimal surface in a space time which is a perturbation over the initial space
time. Using this we perturbatively calculate the changes in HEE upto second
order for boosted black brane like perturbations over $AdS 4$ . 查看全文>>