Hawking Temperature and the Inverse-Radius Scale of the Horizon

Understand

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.