From the BTZ black hole to JT gravity: geometrizing the island

Abstract

We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional point of view. A partial dimensional reduction of AdS${}_3$ in Poincaré coordinates leads to an extremal 2D black hole in JT gravity coupled to a 'bath': the holographic dual of the remainder of the 3D spacetime. Partially reducing the BTZ black hole gives us the finite temperature version. We compute the entropy of the radiation using geodesics in the three-dimensional spacetime. We then focus on the finite temperature case and describe the dynamics by introducing time-dependence into the parameter controlling the reduction. The energy of the black hole decreases linearly as we slowly move the dividing line between black hole and bath. Through a re-scaling of the BTZ parameters we map this to the more canonical picture of exponential evaporation. Finally, studying the entropy of the radiation over time leads to a geometric representation of the Page curve. The appearance of the island region is explained in a natural and intuitive fashion.

22 pages, 5 figures. v2: comments and references added, typos fixed; clarification of dynamics. v3: references added, typos fixed; topological piece of dilaton removed from formulas (results unchanged). v4: version as published in JHEP

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• JT Gravity from Partial Reduction and Defect Extremal Surface
• Defect extremal surfaces for entanglement negativity
• Bounds on gravitational brane couplings and tomography in AdS3 black hole microstates
• Universal Dynamics of Heavy Operators in Boundary CFT${}_2$
• Quasi-normal modes and microscopic description of 2D black holes
• Page Curve and Phase Transition in deformed Jackiw-Teitelboim Gravity
• Unitarity and Page curve for evaporation of 2D AdS black holes
• Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors
• Page Curve from Defect Extremal Surface and Island in Higher Dimensions
• Encoded information of mixed correlations: the views from one dimension higher