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 $\operatorname{ div}T\neq0.$ 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.
Categories: gr-qc