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Euclidean action and the thermodynamics of manifolds without boundary
Phys. Rev. D 41, 3248 – Published 15 May, 1990
DOI: https://doi.org/10.1103/PhysRevD.41.3248
Abstract
I consider general, spherically symmetric spacetimes with cosmological and black-hole horizons. I find that a state of thermal equilibrium may exist in classical manifolds with two horizons as long as a matter distribution is present. The Euclidean action is calculated for general (nonclassical) manifolds without boundary. It is found to equal the grand canonical weighting factor for a spacetime with zero mean thermal energy. I also consider how the Euclidean action is modified by the imposition of fixed-temperature shells in the manifold. I find that the mean thermal energy of the cosmological horizon is negative.
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