2018/03/30 by Partha Paul, Pratik Roy
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/s10714-019-2636-9
19 Pages, 12 Figures, References added
arxiv created 2018/03/30 · arxiv updated 2020/01/08
It is known that the linearized Einstein's equation around the pure AdS can be obtained from the constraint ΔS = Δ< H > , known as the first law of entanglement, on the boundary CFT. The corresponding dual state in the boundary CFT is the vacuum state around which the linear perturbation is taken. In this paper we revisit this question, in the context of AdS3/CFT2 , with the state of the boundary CFT2 as a thermal state. The corresponding dual geometry is a planar BTZ black hole. By considering the linearized perturbation around this black brane we show that Einstein's equation follows from the first law of entanglement. The modular Hamiltonian in a thermal state of the CFT2 that we have used has been recently found in arXiv:1608.01283 [cond-mat.stat-mech].