Holographic equivalence between the first law of entanglement entropy and the linearized gravitational equations

Abstract

We use the intertwining properties of integral transformations to provide a compact proof of the holographic equivalence between the first law of entanglement entropy and the linearized gravitational equations, in the context of the AdS/CFT-correspondence. We build upon the framework developed by Faulkner et al. [1] using the the Wald formalism, and exploit the symmetries of the vacuum modular Hamiltonian of ball-shaped boundary regions.

V4. 11 + 10 pages, 2 figures, in accordance with version as published in PRD

References in corpus (5)

• Towards a derivation of holographic entanglement entropy
• On Holographic Entanglement Entropy and Higher Curvature Gravity
• A Stereoscopic Look into the Bulk
• Equivalent Equations of Motion for Gravity and Entropy
• Entanglement entropy from one-point functions in holographic states

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• Gravity from Entanglement and RG Flow in a Top-down Approach
• Linearized Einstein's Equation around pure BTZ from Entanglement Thermodynamics