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

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.Comment: 10 page

Fermions Tunnelling from Black Holes

We investigate the tunnelling of spin 1/2 particles through event horizons. We first apply the tunnelling method to Rindler spacetime and obtain the Unruh temperature. We then apply fermion tunnelling to a general non-rotating black hole metric and show that the Hawking temperature is recovered.Comment: 22 pages, v2: added references, v3: fixed minor typos, v4: added a new section applying fermion tunnelling method to Kruskal-Szekers coordinates, fixed minor typo, and added references, v5: modified introduction and conclusion, fixed typo

Exact Hawking Radiation of Scalars, Fermions, and Bosons Using the Tunneling Method Without Back-Reaction

Hawking radiation is studied for arbitrary scalars, fermions, and spin-1 bosons, using a tunneling approach, to every order in $\hbar$ but ignoring back-reaction effects. It is shown that the additional quantum terms yield no new contribution to the Hawking temperature. Indeed, it is found that the limit of small $\hbar$ in the standard quantum WKB approximation is replaced by the near-horizon limit in the gravitational WKB approach.Comment: 8 pages, no figures. v3: Introduction updated. Version to appear in PL

There are no quantum corrections to the Hawking temperature via tunneling from a fixed background

It has recently, and repeatedly, been claimed that higher-order quantum corrections to the Hawking temperature can be calculated in a framework where a free particle tunnels from the event horizon of a fixed black hole background. We highlight a few important issues with these claims to finally conclude that no such higher-order corrections exist. Rather, these illusory corrections stem from a misleading definition of the energy