Classically, the laws of black-hole mechanics have the same form as the laws of thermodynamics, but this could have been only a formal analogy. Hawking radiation makes it physical: a stationary black hole emits approximately thermal radiation withso surface gravity is proportional to genuine temperature.
The correspondence is:
- constancy of on a stationary horizon becomes constancy of equilibrium temperature;
- the First law of black-hole mechanics
- Hawking's area theorem becomes a second law, replaced in the quantum theory by the generalized second law for ;
- the impossibility of reaching by a finite process parallels the unattainability of absolute zero.
A real Hawking temperature therefore identifies horizon area as thermodynamic entropy and turns the geometric laws into thermodynamic laws.
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