Lie symmetries of the Ricci and energy-momentum tensors

摘要

Though the Ricci and energy-momentum tensors have the same algebraic symmetries and appear in a similar way in the Einstein equations, in that interchanging them and inverting the gravitational coupling leaves the equations invariant, their differential symmetry Lie algebras are not identical in general. For cylindrically symmetric static spacetimes their inter-relationship is studied in this paper. Neither set of symmetries is a subset of the other in general.