https://doi.org/10.1140/epjp/i2015-15044-2
Regular Article
Ricci inheritance collineation in Bianchi type I spacetimes
Department of Mathematics, University of Peshawar, Peshawar Khyber Pakhtoonkhwa, Pakistan
* e-mail: suhail_74pk@yahoo.com
Received:
10
January
2015
Revised:
16
February
2015
Accepted:
17
February
2015
Published online:
12
March
2015
In this article we explored the Ricci inheritance collineations (RICs) for Bianchi type I spacetimes. When the Ricci tensor is non-degenerate, the general form of vector fields generating the RICs are obtained together with some differential constraints. These differential constraints are then solved to get RICs. In the non-degenerate case, it turns out that the dimension of the Lie algebra of RICs is finite. In the case where the Ricci tensor is degenerate, it is found that the algebra of RICs for Bianchi type I spacetimes is mostly, but not always, infinite dimensional. In one case of degenerate Ricci tensor, we solved the differential constraints completely and a spacetime metric is obtained along with RICs.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2015
