Page curve for an eternal Schwarzschild black hole in a dimensionally reduced model of dilaton gravity

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 backreaction of quantum fields to one-loop order, we solve the semiclassical 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.