Black-hole thermodynamics

Black-hole thermodynamics relates horizon geometry to thermodynamic laws, assigning temperature and entropy to a stationary black hole.

In units $G=\hslash =c=k_B=1$, a stationary black hole with surface gravity $\kappa$ has Hawking temperature $T_H=\kappa /(2\pi )$.

In units $G=\hslash =c=k_B=1$, a black hole of horizon area $A$ has entropy $S_{BH}=A/4$.

For a nonrotating uncharged stationary black hole, the first law is $\delta M=\kappa \delta A/(8\pi )=T_H\delta S_{BH}$.

The physical-process first law derives the area change caused by a small flux of matter through an initially and finally stationary horizon. Linearized Null Raychaudhuri equation evolution converts the Killing-energy flux into $\Delta M=\kappa \Delta A/(8\pi )$.