General relativity, thermodynamics, and the Poincare cycle

Details General relativity, thermodynamics, and the Poincare cycle General relativity, thermodynamics, and the Poincare cycle

Jul 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979natur.280..203t&link_type=abstract

Nature, vol. 280, July 19, 1979, p. 203-205.

Mathematics

14

Cosmology, Poincare Spheres, Relativistic Theory, Relativity, Thermodynamics, Cauchy Problem, Convergence, Entropy, Singularity (Mathematics), Space-Time Functions, Temperature Effects

Scientific paper

The concept of an arbitrarily close return of the universe to a previous initial state, as predicted by the Poincare recurrence theorem, is considered in the context of a closed universe governed by general relativity. With reasonable conditions on global causal structure and the matter tensor, including the time-like convergence condition, it is shown that the corresponding spacetime containing compact Cauchy surfaces cannot be time periodic. The nonrecurrence of a closed general-relativistic universe is attributed to the existence of singularities, which preclude the existence of a finite number of physically distinguishable states. Implications of the nonperiodicity theorem for cosmological models and such thermodynamic concepts as entropy and temperature are discussed.

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