This article is cited in 3 papers

Classification of locally rotationally symmetric Bianchi-I space–times using conformal Ricci collineations

T. Hussain, S. S. Akhtar, F. Khan

Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa, Pakistan

Abstract: We present a complete classification of locally rotationally symmetric (LRS) Bianchi-I space–times in accordance with their conformal Ricci collineations (CRCs). In the case where the Ricci tensor is nondegenerate, we find a general form of the vector field generating CRCs subject to some integrability conditions. Solving the integrability conditions in different cases, we find that the LRS Bianchi-I space–times admit $7$-, $10$-, $11$-, or $15$-dimensional Lie algebras of CRCs in the case where the Ricci tensor is nondegenerate. Moreover, we find that these space–times admit an infinite number of CRCs if the Ricci tensor is degenerate. We give some examples of LRS Bianchi-I space–times that admit nontrivial CRCs and are models of a perfect fluid.

Keywords: conformal Ricci collineation, Ricci collineation, Bianchi-I space–time.

PACS: 04.20.Jb

Received: 26.09.2016
Revised: 16.12.2016

DOI: 10.4213/tmf9279

 English version: Theoretical and Mathematical Physics, 2017, 193:1, 1524–1533

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