Hawking radiation as quantum mechanical reflection

TL;DR

This paper presents a simpler quantum mechanical reflection approach to derive Hawking radiation, providing an exact local calculation of black hole temperature outside the horizon, differing from traditional tunneling methods.

Contribution

It introduces a novel, simpler derivation of Hawking radiation using quantum reflection, avoiding the need to consider regions inside the horizon.

Findings

Reflection coefficient exhibits exponential energy falloff

Derived temperature matches Hawking temperature for spherical black holes

Calculation is entirely outside the horizon, unlike tunneling methods

Abstract

In this article, we explore an alternative derivation of Hawking radiation. Instead of the field-theoretic derivation, we have suggested a simpler calculation based on quantum mechanical reflection from a one-dimensional potential. The reflection coefficient shows an exponential fall in energy which, in comparison with the Boltzmann probability distribution, yields a temperature. The temperature is the same as Hawking temperature for spherically symmetric black holes. The derivation gives an exact local calculation of Hawking temperature that involves a region lying entirely outside the horizon. This is a crucial difference from the tunneling calculation, where it is necessary to involve a region inside the horizon.