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

14 pages latex(2e) iopart style, no figures

References in corpus (4)

• The Many Faces of Gravitoelectromagnetism
• The intrinsic derivative and centrifugal forces in general relativity: II. Applications to circular orbits in some familiar stationary axisymmetric spacetimes
• Spacetime Ehlers group: Transformation law for the Weyl tensor
• General approach to the study of vacuum space-times with an isometry

Cited by in corpus (10)

• The Cotton tensor in Riemannian spacetimes
• On the geometry of Killing and conformal tensors
• On the invariant symmetries of the $\mathcal{D}$-metrics
• Homogeneous Cotton solitons
• Separable geodesic action slicing in stationary spacetimes
• A set of invariant quality factors measuring the deviation from the Kerr metric
• The Simon and Simon-Mars Tensors for Stationary Einstein-Maxwell Fields
• An alternative to the Simon tensor
• Slicing black hole spacetimes
• Relative-observer definition of the Simon tensor