Classification of static plane symmetric space–times according to their matter collineations

Abstract

In this paper we classify static plane symmetric space–times according to their matter collineations. These have been studied for both cases when the energy–momentum tensor is nondegenerate and also when it is degenerate. It turns out that the nondegenerate case yields either four, five, six, seven, or ten independent matter collineations in which four are isometries and the rest are proper. There exists three interesting cases where the energy–momentum tensor is degenerate but the group of matter collineations is finite-dimensional. The matter collineations in these cases are either four, six, or ten.