Tomimura, Nazira A.; Nogales, José A. C. Inhomogeneous model with cosmological term. (English) Zbl 0959.83063 Phys. Lett., A 242, No. 6, 291-295 (1998). 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. Keywords:cosmological term; adiabatic matter production; inhomogeneous Lemaître-Tolman-Bondi metric; hot-big-bang models Citations:Zbl 0668.53062 PDFBibTeX XMLCite \textit{N. A. Tomimura} and \textit{J. A. C. Nogales}, Phys. Lett., A 242, No. 6, 291--295 (1998; Zbl 0959.83063) Full Text: DOI References: [1] Bondi, H., Mon. Not. Roy. Astr. Soc., 107, 410 (1947) [2] S. Weinberg, astro-ph/9610044.; S. Weinberg, astro-ph/9610044. [3] Méndez, V.; Pavon, D., Gen. Rel. Grav., 28, 679 (1996) [4] Prigogine, I.; Geheniau, J.; Gunzig, E.; Nardone, Gen. Rel. Grav., 21, 767 (1989) [5] Lima, J. A.S., Phys. Rev. D, 54, 2571 (1996) [6] Misner, C. W.; Thorne, K. S.; Wheeler, J. A., Gravitation (1973), Freeman: Freeman San Francisco [7] Pavon, D., Phys. Rev. D, 43, 375 (1991) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.