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

TL;DR

This paper investigates the information loss paradox in a (1+1)-dimensional dilaton gravity model derived from four-dimensional Einstein-Hilbert action, demonstrating that the quantum corrected entropy follows the unitary Page curve.

Contribution

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

Findings

Quantum corrections to Hawking temperature computed.

The fine-grained entropy follows the Page curve.

Supports unitarity in black hole evaporation.

Abstract

As a contribution to the subject of the information loss paradox in (1+1)-dimensional gravitational systems, we study a model of (1+1)-dimensional dilaton gravity derived from the four-dimensional Einstein-Hilbert action by dimensional reduction. The reduced action involves the cosmological constant and admits black hole solutions. After including the back-reaction of quantum fields to 1-loop order, we solve the semi-classical field equations perturbatively and compute the quantum correction to the Hawking temperature. We consider the quantum extremal surface approach and invoke the ``island rule'' to compute the fine-grained entropy of the Hawking radiation for an eternal Schwarzschild black hole and demonstrate that it follows the unitary Page curve.