Hawking Radiation Energy and Entropy from a Bianchi-Smerlak Semiclassical Black Hole

TL;DR

This paper examines the relationship between Hawking radiation energy and entropy in semiclassical black holes, comparing it with expectations from unitary quantum evolution in higher dimensions, highlighting where semiclassical and quantum gravity predictions diverge.

Contribution

It analyzes the Bianchi-Smerlak relationship in a 2D model and discusses its applicability and discrepancies in higher-dimensional quantum black hole scenarios.

Findings

The relationship holds well away from entropy peaks and evaporation end.

Discrepancies are due to scattering effects and quantum gravity corrections.

Tiny differences highlight limits of semiclassical approximations.

Abstract

Eugenio Bianchi and Matteo Smerlak have found a relationship between the Hawking radiation energy and von Neumann entropy in a conformal field emitted by a semiclassical two-dimensional black hole. We compare this relationship with what might be expected for unitary evolution of a quantum black hole in four and higher dimensions. If one neglects the expected increase in the radiation entropy over the decrease in the black hole Bekenstein-Hawking A/4 entropy that arises from the scattering of the radiation by the barrier near the black hole, the relation works very well, except near the peak of the radiation von Neumann entropy and near the final evaporation. These discrepancies are calculated and discussed as tiny differences between a semiclassical treatment and a quantum gravity treatment.