Proper Matter Collineations of Plane Symmetric Spacetimes
نویسندگان
چکیده
Let (M, g) be a spacetime, where M is a smooth, connected, Hausdorff four-dimensional manifold and g is smooth Lorentzian metric of signature (+ -) defined on M . The manifold M and the metric g are assumed smooth (C). A smooth vector field ξ is said to preserve a matter symmetry [1] on M if, for each smooth local diffeomorphism φt associated with ξ, the tensors T and φ∗tT are equal on the domain U of φt, i.e., T = φ ∗ tT . Equivalently, a vector field ξ is said to generate a matter collineation if it satisfies the following equation
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