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.Comment: 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, 200
