Complete Einstein equations from the generalized First Law of Entanglement

2017/09/30 by Eunseok Oh, I. Y. Park, Sang-Jin Sin
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Einstein #Entropy (arrow of time) #Law #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum entanglement #Quantum mechanics #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.98.026020

published as Phys. Rev. D 98, 026020 (2018) · 5 pages, 4 figures, v2: title shortened, v4: proof improved. result enhanced v5: result restated as "gravity dual expression of relative entropy is equivalent to Einstein equation"

openalex created_date 2018/01/12 · arxiv created 2018/06/30 · openalex publication_date 2018/07/13 · arxiv updated 2018/07/18 · openalex updated_date 2026/08/05

Abstract

Recently, it was observed that the first law of entanglement leads to the linearized Einstein equation. In this paper, we point out that the gravity dual of an relative entropy expression is equivalent to the full nonlinear Einstein equation. We also construct an entanglement vector field V_E whose flux is the entanglement entropy. The flow of the vector field looks like sewing two space regions along the interface.

Citations

• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Comparison of the Noether charge and Euclidean methods for computing the entropy of stationary black holes
• Thermodynamics of Spacetime: The Einstein Equation of State
• Some properties of the Noether charge and a proposal for dynamical black hole entropy
• Universality of Gravity from Entanglement
• Cool horizons for entangled black holes