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Inhomogeneous model with cosmological term. (English) Zbl 0959.83063

Summary: Some properties of cosmological models with matter creation are investigated in the framework of the Lemaître-Tolman-Bondi (LTB) line element with varying cosmological term. Following [I. Prigogine, J. Gehenian, E. Gunzig and P. Nardone, Gen. Relativ. Gravitation 21, 767-776 (1989; Zbl 0668.53062)] we derive an expression for the flux of entropy as function of chemical potential \(\mu\), the matter creation \(\Psi{}\) and the variation of the cosmological term \(\dot\Lambda\). For adiabatic matter production, the variation of entropy is derived to be proportional to the matter creation rate, \(s^{\alpha}_{;\alpha} = \sigma\Psi\geq 0\) and \(\Psi= -n\dot\Lambda/\widetilde \gamma\kappa\rho\), when one takes into account the state equation \(p = (\widetilde \gamma-1)\rho\). The preceding analysis is applied to the inhomogeneous Lemaître-Tolman-Bondi metric to find a class of hot-big-bang models. The cosmological term was derived from Einstein’s field equations (EFEs) to verify that the universe evolves to a Friedmann-type model when time tends to infinity.

MSC:

83F05 Relativistic cosmology
80A10 Classical and relativistic thermodynamics
83C15 Exact solutions to problems in general relativity and gravitational theory
83C75 Space-time singularities, cosmic censorship, etc.

Citations:

Zbl 0668.53062
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References:

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