The Hawking temperature of a Schwarzschild black hole can be heuristically derived by identifying the temperature with the inverse radius of the horizon up to a multiplicative constant. This does not work for more general black holes such as the Kerr and Reissner-Nordstr\"om solutions. Expounding on the details of how it fails to work nevertheless uncovers interesting connections with the "spring constant" of black holes and with black hole thermodynamics.
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Good et al. (2024) studied this question.
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