Schwarzschild Spacetime Thermodynamics

Abstract

Bardeen, Carter, and Hawking presented the four laws of black hole mechanics in 1973. Only 45 years later, Wang and Braunstein rigorously demonstrated that surfaces away from horizons are not thermodynamic, unless they are spherically symmetric, meaning that black hole thermodynamics can only be generalized to surfaces that are concentric with black hole horizons. This generalization, however, can be straightforwardly achieved with a twist: By equating two temperature definitions that should simultaneously hold for an equilibrium thermodynamics of spacetime’s degrees of freedom, it is immediately found that the latter only applies to surfaces with constant Newtonian gravitational potential. The laws of thermodynamics can correspondingly be rephrased in terms of Schwarzschild spacetime’s state variables at these surfaces.

Keywords: black hole mechanics, thermodynamics, Schwarzschild spacetime