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Complete Einstein equation from the generalized First Law of Entanglement

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arxiv 1709.05752 v5 pith:SL4TXIKF submitted 2017-09-18 hep-th gr-qc

Eunseok Oh (Hanyang) , I.Y. Park (Philander Smith College) , Sang-Jin Sin (Hanyang) This is my paper · ORCID
classification hep-thgr-qc
keywords entanglementeinsteinequationentropyfieldfirstvectoralong
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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 non-linear 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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Timelike Entanglement First Law and Linearized Field Equations in Higher Curvature Gravity

    hep-th 2026-07 unverdicted novelty 6.0 of 10

    Timelike entanglement first law holds in Lovelock gravity about AdS, with both entropy and modular Hamiltonian variations carrying the same coupling factor that renormalizes Newton's constant in the linearized equations.

  2. Entanglement first law for timelike entanglement entropy and linearized Einstein's equation

    hep-th 2025-11 conditional novelty 6.0 of 10

    For timelike boundary regions, the entanglement first law ΔS = Δ⟨H⟩ is equivalent, by the paper's proof, to the linearized Einstein equations around AdS.

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