Page curves for a family of exactly solvable evaporating black holes

TL;DR

This paper analyzes entanglement entropy and Page curves in a family of exactly solvable 2D black hole models, revealing how islands and transitions behave in evaporating and glued geometries, and discussing related paradoxes.

Contribution

It introduces a family of solvable models for black hole evaporation, studies island dynamics, and explores effects of gluing different black hole solutions on Page curves and entropy transitions.

Findings

Page transition occurs at one-third of black hole lifetime in evaporating solutions.

Gluing black hole geometries causes the Page transition to split into two separate events.

The study highlights issues with purification rates and radiation paradoxes.

Abstract

We study the entanglement entropy of a one-parameter family of exactly solvable gravities in the 2-dimensional asymptotically-flat space. The islands and Page curves of eternal, evaporating and bath-removed black holes are investigated. The different theories in this parameter class are identified through field redefinitions which leave the island invariant. The Page transition is found to occur at the first a third of the black hole life time in the evaporating case for this family of solutions. In addition, we consider gluing the equilibrium black hole and the evaporating one along a null trajectory and study the effect of gluing on the islands and Page curves. In the glued space, the island jumps across two different geometries at a certain retarded time. As a result, the Page transition is stretched and split into two separate ones -- the first transition happens when the net entropy generation stops and the second one occurs as the early radiation effectively starts to become purified. Finally, we discuss the issues concerning the inconsistent rates of purification and the paradox related to the state of the radiation.