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By studying the Hawking radiation of the most general static sphericallysymmetric black hole arising from scalar and Dirac particles tunnelling, wefind the Hawking temperature is invariant in the general coordinaterepresentation (\ref{arbitrary1}), which satisfies two conditions: a) itsradial coordinate transformation is regular at the event horizon; and b) thereis a time-like Killing vector.

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