Black Holes, Hawking Radiation and the Information Paradox

TL;DR

This paper explores the quantum properties of scalar fields around Schwarzschild black holes, reproduces Hawking radiation, and discusses the nature of black hole entropy and potential implications near the singularity.

Contribution

It introduces a novel approach to defining a system that mimics black hole thermodynamics but challenges the classical interpretation of entropy.

Findings

Reproduces Hawking temperature and energy flux.

Identifies a system with entropy proportional to horizon area that may not have a classical entropy.

Suggests unusual behavior near the black hole singularity.

Abstract

This talk is about results obtained by Kirill Melnikov and myself pertaining to the canonical quantization of a massless scalar field in the presence of a Schwarzschild black hole. After a brief summary of what we did and how we reproduce the familiar Hawking temperature and energy flux, I focus attention on how our discussion differs from other treatments. In particular I show that we can define a system which fakes an equilibrium thermodynamic object whose entropy is given by the $A/4$ (where $A$ is the area of the black hole horizon), but for which the assignment of a classical entropy to the system is incorrect. Finally I briefly discuss a discretized version of the theory which seems to indicate that things work in a surprising way near $r=0$.