Regularizing tunnelling calculations of Hawking temperature

TL;DR

This paper demonstrates that proper regularization of singular integrals in tunnelling calculations ensures consistent Hawking temperature results across different coordinate systems, including isotropic radial coordinates.

Contribution

It introduces a regularization method that corrects apparent discrepancies in Hawking temperature calculations across various coordinate choices.

Findings

Regularization restores the standard Hawking temperature in isotropic coordinates.

Coordinate transformations do not alter the physical Hawking temperature when regularized properly.

The method applies to smooth radial coordinate transformations, confirming their physical equivalence.

Abstract

Attempts to understand Hawking radiation as tunnelling across a black hole horizon require the consideration of singular integrals. Although Schwarzschild coordinates lead to the standard Hawking temperature, isotropic radial coordinates may appear to produce an incorrect value. It is demonstrated here how the proper regularization of singular integrals leads to the standard temperature for the isotropic radial coordinates as well as for other smooth transformations of the radial variable, which of course describe the same black hole.