Method of complex paths and general covariance of Hawking radiation

TL;DR

This paper demonstrates that Hawking radiation is covariant across different coordinate systems by applying the complex path method to regularize horizon singularities, confirming its coordinate-invariant nature.

Contribution

It introduces the use of complex paths to derive Hawking radiation in non-standard coordinates, showing the covariance of the phenomenon.

Findings

Hawking radiation is recovered in various coordinate systems without horizon singularities.

The method regularizes the semi-classical action's horizon singularity.

Hawking radiation's particle spectrum is not directly linked to detector responses.

Abstract

We apply the technique of complex paths to obtain Hawking radiation in different coordinate representations of the Schwarzschild space-time. The coordinate representations we consider do not possess a singularity at the horizon unlike the standard Schwarzschild coordinate. However, the event horizon manifests itself as a singularity in the expression for the semi-classical action. This singularity is regularized by using the method of complex paths and we find that Hawking radiation is recovered in these coordinates indicating the covariance of Hawking radiation. This also shows that there is no correspondence between the particles detected by the model detector and the particle spectrum obtained by the quantum field theoretic analysis -- a result known in other contexts as well.