Bianchi I with variable $G$ and $\Lambda$. Self-Similar approach

Abstract

In this paper we study how to attack under the self-similarity hypothesis a perfect fluid Bianchi I model with variable $G,$and $\Lambda ,$ but under the condition $\mathrm{div}T\ne 0.$ We arrive to the conclusion that: $G$ and $\Lambda$ are decreasing time functions (the sing of $\Lambda$ depends on the equation of state), while the exponents of the scale factor must satisfy the conditions ${\sum }_{i=1}^3{\alpha }_i=1$ and ${\sum }_{i=1}^3{\alpha }_i^2<1,$ $\forall \omega \in (-1,1),$ relaxing in this way the Kasner conditions. We also show the connection between the behavior of $G$ and the Weyl tensor.

15 pages. accepted in IJMPA

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