Page Curve for an Evaporating Schwarzschild Black Hole in Dimensionally-Reduced Model of Dilaton Gravity

TL;DR

This paper demonstrates that in a (1+1)-dimensional dilaton gravity model derived from four-dimensional Einstein-Hilbert action, the entanglement entropy of Hawking radiation follows the Page curve, indicating unitary evolution during black hole evaporation.

Contribution

It applies the island rule and quantum extremal surface approach to a dimensionally-reduced model, showing the Page curve in an evaporating black hole scenario.

Findings

The entanglement entropy follows the Page curve during evaporation.

The model exhibits both eternal and evaporating black hole solutions.

Hawking radiation evolution is shown to be unitary.

Abstract

We study entanglement entropy of quantum fields in a (1+1)-dimensional model of dilaton gravity derived from the four-dimensional Einstein-Hilbert action by dimensional reduction. Scalar matter is coupled to gravity, while the back-reaction is included via the Polyakov-Liouville action. This theory exhibits both eternal and evaporating Schwarzschild black hole solutions. The fine-grained entropy in a collapse scenario is investigated by applying the "island rule" via the quantum extremal surface approach. We demonstrate that the fine-grained entropy of the Hawking radiation follows the Page curve, and therefore the evolution of the Hawking radiation is unitary.