The Cotton, Simon-Mars and Cotton-York Tensors in Stationary Spacetimes

TL;DR

This paper investigates the properties and relationships of the Cotton-York and Simon-Mars tensors in stationary vacuum spacetimes, using the congruence approach to better understand their connection to the Kerr spacetime and related geometric structures.

Contribution

It introduces a congruence-based framework to analyze the Cotton-York and Simon-Mars tensors, linking them to the Papapetrou field and principal null directions in stationary spacetimes.

Findings

Established relationships between the tensors and the Papapetrou field.

Connected tensor properties to the characterization of Kerr spacetime.

Provided a clearer geometric interpretation of these tensors in stationary contexts.

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 of the principal null directions of the Weyl tensor with those of the Papapetrou field are also investigated in this more transparent language.