The Cotton, Simon–Mars and Cotton–York tensors in stationary spacetimes

Abstract

The Cotton–York and Simon–Mars tensors in stationary vacuum spacetimes are studied in the language of the congruence approach pioneered by Hawking and Ellis. Their relationships with the Papapetrou field defined by the stationary Killing congruence and with a recent characterization of the Kerr spacetime in terms of the alignment between the principal null directions of the Weyl tensor with those of the Papapetrou field are also investigated in a more transparent language.