Hawking Radiation as Tunneling

TL;DR

This paper provides a straightforward derivation of Hawking radiation as a tunneling phenomenon, emphasizing conservation laws and resulting in a non-thermal spectrum, with comparisons to charged particle emission.

Contribution

It offers a direct derivation of Hawking radiation as tunneling, incorporating conservation laws and analyzing the resulting non-thermal spectrum.

Findings

Hawking radiation can be derived as a tunneling process.

The spectrum deviates from perfect thermality due to conservation laws.

Comparison with charged particle emission highlights differences in spontaneous emission processes.

Abstract

We present a short and direct derivation of Hawking radiation as a tunneling process, based on particles in a dynamical geometry. The imaginary part of the action for the classically forbidden process is related to the Boltzmann factor for emission at the Hawking temperature. Because the derivation respects conservation laws, the exact spectrum is not precisely thermal. We compare and contrast the problem of spontaneous emission of charged particles from a charged conductor.