Equivalent Equations of Motion for Gravity and Entropy

Abstract

We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter pace. In doing so, we make use of the formalism of kinematic space [arXiv:1505.05515] and fields on this space, introduced in [arXiv:1604.03110]. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.

7+4 pages, 3 figures

References in corpus (3)

• Towards a derivation of holographic entanglement entropy
• Tomography from Entanglement
• Deriving the First Law of Black Hole Thermodynamics without Entanglement