ON THE THERMODYNAMICS OF SIMPLE NONISENTROPIC PERFECT FLUIDS IN GENERAL-RELATIVITY

We examine the consistency of the thermodynamics of irrotational and n on-isentropic perfect fluids complying with matter conservation by loo king at the integrability conditions of the Gibbs-Duhem relation. We s how that the latter is always integrable for fluids of the following t ypes: (i) static, (ii) isentropic (admits a barotropic equation of sta te) and (iii) the source of a spacetime for which r greater than or eq ual to 2, where r is the dimension of the orbit of the isometry group. This consistency scheme is also tested in two large classes of known exact solutions for which r i 2, in general: perfect fluid Szekeres so lutions (classes I and II). In none of these cases is the Gibbs-Duhem relation integrable, in general, though specific particular cases of S zekeres class II (all complying with r < 2) are identified for which t he integrability of this relation can be achieved. We show that Szeker es class I solutions satisfy the integrability conditions only in two trivial cases, namely the spherically symmetric limiting case and the Friedman-Robertson-Walker (FRW) cosmology. Explicit forms of the state variables and equations of state linking them are given and discussed in relation to the FRW limits of the solutions. We show that fixing f ree parameters in these solutions by a formal identification with FRW parameters leads, in all cases examined, to unphysical temperature evo lution laws, quite unrelated to those of their FRW limiting cosmologie s.