Symmetries of the energy–momentum tensor of spherically symmetric Lorentzian manifolds

Abstract

Matter collineations of spherically symmetric Lorentzian manifolds are considered. These are investigated when the energy–momentum tensor is nondegenerate and also when it is degenerate. We have classified space–times admitting higher symmetries and space–times admitting SO(3) as the maximal isometry group. For the nondegenerate case, we obtain either four, six, seven, or ten independent matter collineations in which four are isometries and the rest are proper. The results of the previous paper [Sharif and Sehar (Gen. Relativ. Gravit. 35, 1091 (2003)] are recovered as a special case. It is worth noting that we have also obtained two cases where the energy–momentum tensor is degenerate but the group of matter collineations is finite-dimensional, i.e., four or ten.