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Then

H.Z. Chen, R.C. Myers, D. Neuenfeld, I.A. Reyes and J. Sandor, Quantum Extremal Islands Made Easy, Part II: Black Holes on the Brane , JHEP 12
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2021

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

Verheijden, Evita, Verlinde, Erik

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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 Poincar\'e 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.