Note on Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes
Pantelis S. Apostolopoulos, Michael Tsamparlis
TL;DR
This paper revises the classification of Kantowski-Sachs and Bianchi Types I and III spacetimes with Matter Collineations, providing a complete Lie algebra of MCs and constraints on the Einstein tensor when non-degenerate.
Contribution
It offers a complete classification of Matter Collineations for these spacetimes, correcting and extending previous incomplete results.
Findings
Complete Lie algebra of MCs derived for non-degenerate Einstein tensor cases.
Identified algebraic constraints on the spatial components of the Einstein tensor.
Revised classification improves understanding of symmetries in these spacetimes.
Abstract
We show that the classification of Kantowski-Sachs, Bianchi Types I and III spacetimes admitting Matter Collineations (MCs) presented in a recent paper by Camci et al. [Camci, U., and Sharif, M. {Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes}, 2003 Gen. Relativ. Grav. vol. 35, 97-109] is incomplete. Furthermore for these spacetimes and when the Einstein tensor is non-degenerate, we give the complete Lie Algebra of MCs and the algebraic constraints on the spatial components of the Einstein tensor.
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