Classification of LRS Bianchi type I Spacetimes via Conformal Ricci Collineations
Abstract
In this paper, we present a complete classification of Locally Rotationally Symmetric (LRS) Bianchi type I spacetimes according to their Conformal Ricci Collineations (CRCs). When the Ricci tensor is non-degenerate, a general form of the vector field generating CRCs is found, subject to some integrability conditions. Solving the integrability conditions in different cases, it is found that the LRS Bianchi type I spacetimes admit 7, 10, 11 or 15- dimensional Lie algebra of CRCs for the choice of non-degenerate Ricci tensor. Moreover, it is found that these spacetimes admit infinite number of CRCs when the Ricci tensor is degenerate. Some examples of perfect fluid LRS Bianchi type I spacetime metrics are provided admitting non trivial CRCs.
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Cite
@article{arxiv.1701.06900,
title = {Classification of LRS Bianchi type I Spacetimes via Conformal Ricci Collineations},
author = {Tahir Hussain and Sumaira Saleem Akhtar and Fawad Khan},
journal= {arXiv preprint arXiv:1701.06900},
year = {2018}
}
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24 pages