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

TL;DR

This paper explores the evaporation process of 2D black holes in JT gravity by analyzing their 3D BTZ counterparts, providing a geometric interpretation of the Page curve and the island phenomenon.

Contribution

It introduces a 3D perspective on 2D black hole evaporation, connecting BTZ black holes to JT gravity and elucidating the emergence of the island and Page curve geometrically.

Findings

Geometric derivation of the Page curve in JT gravity.

Natural explanation of the island region emergence.

Mapping of black hole evaporation to BTZ parameters.

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 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. 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.