Physics of Relativistic Perfect Fluids

A criterion is presented and discussed to detect when a divergence-free perfect fluid energy tensor in the space-time describes an evolution in local thermal equilibrium. This criterion is applied to the class II Szafron-Szekeres perfect fluid space-times solutions, giving a very simple characterization of those that describe such thermal evolutions. For all of them, the significant thermodynamic variables are explicitly obtained. Also, the specific condition is given under which the divergence-free perfect fluid energy tensors may be interpreted as an ideal gas. 1 Physical fluids and energetic evolutions. The inverse problem In the absence of nuclear or chemical reactions, and independent of the external constraints to which it may be submitted, a material medium is considered here as physically characterized by the specification of its molecular components. In a domain Ω of the space-time, and in the absence of exterior constraints, every initial configuration of a material medium gives rise to a particular evolution. And, to every one of these evolutions in Ω an energy tensor [1] Tf corresponds univocally. Due to the absence of exterior constraints, the energy tensors so obtained are divergence-free, ∇ · Tf = 0. Thus, a set Tf ≡ {Tf} of energy tensors is associated to every medium f, namely those of all its possible unconstrained evolutions in the space-time domain Ω. We have the diagram of Figure 1. The energetic description of a particular evolution of the medium f by the energy tensor Tf, consists, and only consists, of the specification of the energy density ρf, the energy flow density qf and the stress tensor tf of this evolution of f in Ω.