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.

24 pages

References in corpus (5)

• Ricci Collineations of the Bianchi Types I and III, and Kantowski-Sachs Spacetimes
• Ricci Collineations of the Bianchi Type II, VIII, and IX Space-times
• Conformal Ricci collineations of static spherically symmetric spacetimes
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Cited by in corpus (1)

• Conformal symmetries of the energy-momentum tensor of spherically symmetric static spacetimes