Comments on anomaly versus WKB/tunneling methods for calculating Unruh radiation

TL;DR

This paper critically compares the anomaly and WKB/tunneling methods for calculating Unruh radiation, revealing limitations in anomaly methods and emphasizing the importance of temporal contributions in tunneling calculations.

Contribution

It demonstrates that anomaly methods do not reliably produce the correct Unruh temperature and highlights the necessity of considering temporal contributions in tunneling approaches.

Findings

Anomaly methods often give incorrect Unruh temperatures.

Tunneling method requires accounting for temporal contributions.

Discrepancies exist between consistent and covariant anomaly approaches.

Abstract

In this Letter we make a critique of, and comparison between, the anomaly method and WKB/tunneling method for obtaining radiation from non-trivial spacetime backgrounds. We focus on Rindler spacetime (the spacetime of an accelerating observer) and the associated Unruh radiation since this is the prototype of the phenomena of radiation from a spacetime, and it is the simplest model for making clear subtle points in the tunneling and anomaly methods. Our analysis leads to the following conclusions: (i) neither the consistent and covariant anomaly methods gives the correct Unruh temperature for Rindler spacetime and in some cases (e.g. de Sitter spacetime) the consistent and covariant methods disagree with one another; (ii) the tunneling method can be applied in all cases, but it has a previously unnoticed temporal contribution which must be accounted for in order to obtain the correct temperature.