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 AdS3 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.
Highlights
Surface (QES) [7], the surface that minimizes the generalized entropy, to monitor the evolution of the entropy of the evaporating black hole
We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional point of view
Since the quantum mechanical model has a finite temperature, its dual is given by a two-dimensional AdS black hole
Summary
Jackiw-Teitelboim (JT) gravity is a two-dimensional dilaton gravitational theory (see [22, 23] for the original model, and [24, 25] for compact reviews). The general solution for the metric is ds. The action (2.1) admits black hole solutions, dynamically formed by throwing in matter from the boundary. 4πG κ is an integration constant that specifies the asymptotic boundary conditions of the dilaton field (notice that Φ is dimensionless, but Φr has dimensions of length). In terms of the lightcone coordinates (u, v), the metric and dilaton profile are. Note that if we take the limit E → 0 we recover the AdS2 geometry in Poincaré coordinates and the corresponding dilaton profile: 2Φr (X+ − X−). Since E → 0 sets the Hawking temperature TH → 0, we will interpret this solution as the extremal AdS2 black hole. We will see how to obtain these black holes from three dimensional Anti-de Sitter space
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