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arXiv · 1710.01316

Metric Perturbations of Extremal Surfaces

Benjamin Mosk
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Abstract

Motivated by the HRRT-formula for holographic entanglement entropy, we consider the following question: what are the position and the surface area of extremal surfaces in a perturbed geometry, given their anchor on the asymptotic boundary? We derive explicit expressions for the change in position and surface area, thereby providing a closed form expression for the canonical energy. We find that a perturbation governed by some small parameter $\lambda$ yields an expansion of the surface area in terms of a highly non-local expression involving multiple integrals of geometric quantities over the original extremal surface.

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Benjamin Mosk. 2017-10-03. Metric Perturbations of Extremal Surfaces. https://doi.org/10.1088/1361-6382/aaa4e9

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