Equivalence of the Hawking temperature in conformal frames

TL;DR

This paper demonstrates that the Hawking temperature remains invariant under certain conformal transformations for specific black hole solutions, using multiple semiclassical calculation methods.

Contribution

It provides a semiclassical verification of the conformal invariance of Hawking temperature for a particular class of black holes, extending previous conjectures.

Findings

Hawking temperature is invariant under specific conformal transformations.

Multiple methods (Bogoliubov coefficients, Euclideanization, reflection coefficient, gravitational anomaly) yield consistent results.

The invariance holds for a simple symmetrical, non-asymptotically flat black hole.

Abstract

The conformal invariance of the Hawking temperature, conjectured for the asymptotically flat and stationary black holes by Jacobson and Kang, is semiclassically evaluated for a simple particular case of symmetrical spherically and non asymptotically flat black hole. By using the Bogoliubov coefficients, the metric euclideanization, the reflection coefficient and the gravitational anomaly, as methods of calculating the Hawking temperature, we find that it is invariant under a specific conformal transformation of the metric. We discuss briefly the results for each method.