What kinds of coordinate can keep the Hawking temperature invariant for the static spherically symmetric black hole?

TL;DR

This paper demonstrates that the Hawking temperature remains invariant under a broad class of coordinate transformations for static spherically symmetric black holes, provided certain regularity and symmetry conditions are met.

Contribution

It establishes the invariance of Hawking temperature under general coordinate changes that are regular at the horizon and admit a time-like Killing vector.

Findings

Hawking temperature is invariant under specific coordinate transformations.

The invariance holds for scalar and Dirac particles tunnelling.

Conditions include regularity at the horizon and existence of a time-like Killing vector.

Abstract

By studying the Hawking radiation of the most general static spherically symmetric black hole arising from scalar and Dirac particles tunnelling, we find the Hawking temperature is invariant in the general coordinate representation (\ref{arbitrary1}), which satisfies two conditions: a) its radial coordinate transformation is regular at the event horizon; and b) there is a time-like Killing vector.