Thermal equilibrium in general relativity and the special nature of the cosmological constant

Abstract

The problem of thermal equilibrium in general relativity is discussed and the unique role played by the fluid associated with the cosmological constant is emphasized. In addition to being the only fluid that is always in thermal equilibrium, it is shown here that its energy can also be seen as a universal quantity given by $E_Λ=ρ_ΛV$, where $V$ is a spatial volume. Furthermore, if the cosmological constant turns out to be a universal constant, then the conclusion that any spatial volume $V$ has an intrinsic energy follows naturally from the approach considered here. A possible application to quantum theories of gravity that postulate the existence of a minimal length scale is discussed. In studying the energies, the so-called teleparallel equivalent of general relativity is used, and the difficulty with the zero-point energy is discussed in light of the gravitational energy problem. The quasi-local energies of the Reissner-Nordström-de Sitter black hole and of a regular black hole are calculated. The results obtained here with the teleparallel theory are consistent with our expectations.