Black Hole Thermodynamics

The set of laws governing black hole dynamics when interpreted in light of their correspondence with the ordinary four laws of thermodynamics, which is as follows.

Zeroth law. In a black hole the surface gravity , κ, is constant at the event horizon ; this is reminiscent of thermodynamics were all parts of a system at thermodynamical equilibrium have the same temperature, T, and suggests a parallelism between (κ /2π) and T.

First law. Under perturbations the variations of the mass M, charge Q, angular momentum J and area A of a stationary black hole are related by

ω and ϕ being the angular velocity and the co-rotating electric potential at the horizon; this is reminiscent of the way in which the variation of the internal energy U of a thermodynamic system at temperature T and pressure P is related to the variation of entropy S and volume V: dU = TdS − PdV. Moreover the above suggested relation (κ /2π) ⇔ T, here also supported by the correspondences (A/4) ⇔ S, M ⇔ U, receives a...