Hawking radiation in different coordinate settings: Complex paths approach

TL;DR

This paper demonstrates that Hawking radiation can be derived in various coordinate systems of Schwarzschild spacetime using the complex paths method, confirming its coordinate invariance.

Contribution

It extends the complex paths approach to coordinate systems without horizon singularities, showing Hawking radiation is consistent across different representations.

Findings

Hawking radiation is recovered in multiple coordinate systems.

The method regularizes horizon singularities in the semiclassical action.

Hawking radiation's covariance is confirmed in different coordinates.

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 semiclassical 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 as far as these coordinates are concerned.