Doctoral Committee Review Talk 11 am  12 noon, Lecture Hall 2 Einstein's Equations from Entanglement Thermodynamics Pratik Roy Chennai Mathematical Institute. 250418 Abstract It is known that linearized Einstein equation around pure AdS can be obtained from the constraint ∆S = ∆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. We revisit this question, in the context of AdS_3 /CFT_2, with the boundary CFT_2 in a thermal state. The corresponding dual geometry is a planar BTZ black hole. By considering the linearized perturbation around the black brane, we show that Einstein’s equation follows from the first law of entanglement.
