Hawking Radiation as Quantum Tunneling in Rindler Coordinate

TL;DR

This paper demonstrates that Hawking radiation can be understood as quantum tunneling in Rindler spacetime, providing a unified approach to various black hole and cosmological horizons using local Rindler coordinates.

Contribution

It introduces a method to derive Hawking radiation as tunneling in Rindler coordinates applicable to multiple black hole types and cosmological horizons.

Findings

Correct Boltzmann factor obtained from contour integral

Applicable to Schwarzschild, Reissner-Nordström, Kerr black holes

Extended to de Sitter and anti-de Sitter spaces

Abstract

We substantiate the Hawking radiation as quantum tunneling of fields or particles crossing the horizon by using the Rindler coordinate. The thermal spectrum detected by an accelerated particle is interpreted as quantum tunneling in the Rindler spacetime. Representing the spacetime near the horizon locally as a Rindler spacetime, we find the emission rate by tunneling, which is expressed as a contour integral and gives the correct Boltzmann factor. We apply the method to non-extremal black holes such as a Schwarzschild black hole, a non-extremal Reissner-Nordstr\"{o}m black hole, a charged Kerr black hole, de Sitter space, and a Schwarzschild-anti de Sitter black hole.