Symmetries of the Energy-Momentum Tensor for Kantowski-Sachs Spacetimes

This article investigates matter collineations (MCs) within KantowskiSachs spacetimes, examining the stress-energy tensor in both its contravariant and mixed representations. We solved the MC equations under two scenarios: when the energy-momentum tensor is non-degenerate and when it is degenerate. In the case of a degenerate energy-momentum tensor, we utilize a direct integration method to tackle the MC equations, leading to the establishment of an infinite-dimensional Lie algebra. Conversely, when dealing with a non-degenerate energy-momentum tensor, the contravariant formulation yields a finite-dimensional Lie algebra, with dimensions 4, 6, 7 or 10. However, for the mixed form of the energy-momentum tensor, the dimension of the Lie algebra becomes infinite.