Thermodynamic class II Szekeres-Szafron solutions. Singular models

Abstract

A family of parabolic Szekeres-Szafron class II solutions in local thermal equilibrium is studied and their associated thermodynamics are obtained. The subfamily with the hydrodynamic behavior of a generic ideal gas (defined by the equation of state $p=kn\Theta$) results to be an inhomogeneous generalization of flat FLRW $\gamma$-law models. Three significative interpretations that follow on from the choice of three specific thermodynamic schemes are analyzed in depth. First, the generic ideal gas in local thermal equilibrium; this interpretation leads to an inhomogeneous temperature $\Theta$. Second, the thermodynamics with homogeneous temperature considered by Lima and Tiomno (CQG 6 1989). And third, a new model having exactly the homogeneous temperature of the FLRW limit. It is shown that the three models above fulfill the necessary macroscopic requirements for physical reality (positivity of matter density and temperature, energy conditions and compressibility conditions) in wide domains of the spacetime.

arXiv comment22 pages, 1 figure

References in corpus (7)

• Inhomogeneous cosmological models: exact solutions and their applications
• Entropy in Poincaré gauge theory: Hamiltonian approach
• Symmetry and Equivalence in Szekeres Models
• Intrinsic, deductive, explicit, and algorithmic characterization of the Szekeres-Szafron solutions
• Relativistic perfect fluids in local thermal equilibrium
• On the Thermodynamics of Simple Non-Isentropic Perfect Fluids in General Relativity
• Frame Rotation in the Szekeres Spacetimes

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• On the flow of perfect energy tensors
• Thermodynamics of the universes admitting isotropic radiation
• Thermodynamic Interpretation of the Kompanneets-Chernov-Kantowski-Sachs Solutions