Abstract
The vector fields along which the metric, the Ricci and the energy-momentum tensors remain invariant under the Lie transport are called the vectors (KVs), the Ricci collineations (RCs) and the matter collineations(MCs), respectively. In this paper we show that the solution of the Killing equations for a second-rank, diagonal, symmetric tensor for which two components are equal provides an algorithm from which we can find the exact nature of KVs, RCs and MCs, and the dimension of the Lie algebras generated by them for all plane-symmetric static space-times.
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