Stationary spacetimes and the Simon tensor

Abstract

For stationary vacuum spacetimes the Bianchi identities of the second kind equate the Simon tensor to the Simon-Mars tensor, the latter having a clear geometrical interpretation. The equivalence of these two tensors is broken in the nonvacuum case by additional source energy-momentum terms, but absorbing these source terms into a redefinition of the Simon tensor restores the equality. Explicit examples are discussed for electrovacuum and rigidly rotating matter fields.

To appear on the Proceedings of the International Conference in Honor of Y. Choquet-Bruhat, "Analysis, Manifolds, and Geometric Structures in Physics" Hotel Cala di Mola Porto Azzurro - Isola d'Elba June 24th-26th, 2004