A Canonical Hamiltonian Derivation of Hawking Radiation

TL;DR

This paper derives Hawking radiation through canonical quantization in Lemaitre coordinates, emphasizing the time-dependent Hamiltonian and demonstrating unitarity in the evolution of the massless scalar field around a Schwarzschild black hole.

Contribution

It provides a canonical Hamiltonian derivation of Hawking radiation highlighting the importance of time dependence and unitarity, differing from traditional approaches.

Findings

Hawking radiation can be derived from a time-dependent Hamiltonian.

The evolution of the massless field is unitary despite thermal flux.

Lemaitre coordinates are effective for this derivation.

Abstract

We present a derivation of Hawking radiation based on canonical quantization of a massless scalar field in the background of a Schwarzschild black hole using Lemaitre coordinates and show that in these coordinates the Hamiltonian of the massless field is time-dependent. This result exhibits the non-static nature of the problem and shows it is better to talk about the time dependence of physical quantities rather than the existence of a time-independent vacuum state for the massless field. We then demonstrate the existence of Hawking radiation and show that despite the fact that the flux looks thermal to an outside observer, the time evolution of the massless field is unitary.