Hawking radiation in a non-covariant frame: the Jacobi metric approach

TL;DR

This paper reformulates Hawking temperature derivation for static and stationary black holes using the non-covariant Jacobi metric, simplifying calculations by avoiding complexities of covariant approaches.

Contribution

It introduces a novel Jacobi metric approach that streamlines Hawking temperature calculations without relying on covariant metric forms.

Findings

Jacobi metric simplifies Hawking temperature derivation.

The approach avoids issues with energy modes and metric signature changes.

Results are obtained with less computational complexity.

Abstract

The present paper deals with a reformulation of the derivation of Hawking temperature for static and stationary black holes. In contrast to the conventional approach, where the covariant form of the metrics are used, we use the manifestly non-covariant Jacobi metric for the black holes in question. In the latter, a restricted form of Hamilton-Jacobi variational principle is exploited where the energy of the particle (pertaining to Hawking radiation) appears explicitly in the metric as a constant parameter. Our analysis shows that, as far as computation of Hawking temperature (for stationary black holes) is concerned, the Jacobi metric framework is more streamlined and yields the result with less amount of complications, (as for example, considerations of positive and negative energy modes and signature change of the metric across horizon do not play any direct role in the present analysis).