The mathematical study of symmetry in general relativity
The concept of symmetry in general relativity (GR) is discussed from a mathematical point of view (predominantly geometrical). The topics covered are: projective symmetry (including affine, homothetic and Killing symmetries), conformal symmetry and symmetries of the Ricci, energy-momentum and curvature tensors. The sectional curvature in GR is also studied in detail. The main emphasis is put on the more general theorems available in differential geometry rather than on specific examples. The possibility of extension of the group action to a global (Lie) group on a 4-dimensional spacetime manifold is also analyzed. It is suggested that these results can be used in GR to extend locally observed cosmological symmetries to global symmetries.
scientific article; zbMATH DE number 1486802