A Canonical Hamiltonian Derivation of Hawking Radiation

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.