Ricci and matter collineations in space-time
Let \(M\) be a spacetime manifold with Lorentz metric \(g\). Various symmetries arise in the exact solutions of Einstein's field equations given by \(G_{ab} \equiv R_{ab} - {1\over 2} Rg_{ab} = \kappa T_{ab}\), where \(G_{ab}\), \(R_{ab}\), and \(T_{ab}\) are components of the Einstein tensor, the Ricci tensor, and the matter (or energy-momentum) tensor, respectively. A vector field \(X\) on \(M\) is called a matter collineation if \({\mathfrak L}_X T_{ab} = 0\) and a Ricci collineation if \({\mathfrak L}_X R_{ab} = 0\). In this paper, the authors study Ricci and matter collineations. They give a mathematical description of their dimensionality, differentiability, extendibility etc., and construct examples of Ricci collineations in decomposable spacetimes.
scientific article; zbMATH DE number 877795
scientific article