Search results for "Cotton tensor"

showing 2 items of 2 documents

Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

2003

We analyze type I vacuum solutions admitting an isometry whose Killing 2--form is aligned with a principal bivector of the Weyl tensor, and we show that these solutions belong to a family of type I metrics which admit a group $G_3$ of isometries. We give a classification of this family and we study the Bianchi type for each class. The classes compatible with an aligned Killing 2--form are also determined. The Szekeres-Brans theorem is extended to non vacuum spacetimes with vanishing Cotton tensor.

Weyl tensorPhysicsClass (set theory)Physics and Astronomy (miscellaneous)Group (mathematics)Cotton tensorFOS: Physical sciencesGeneral Relativity and Quantum Cosmology (gr-qc)Type (model theory)General Relativity and Quantum Cosmologysymbols.namesakeGeneral Relativity and Quantum CosmologyHomogeneous spaceIsometrysymbolsMathematics::Differential GeometryBivectorMathematical physics
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Gravito-magnetic vacuum spacetimes: kinematic restrictions

2003

We show that there are no vacuum solutions with a purely magnetic Weyl tensor with respect to an observer submitted to kinematic restrictions involving first order differential scalars. This result generalizes previous ones for the vorticity-free and shear-free cases. We use a covariant approach which makes evident that only the Bianchi identities are used and, consequently, the results are also valid for non vacuum solutions with vanishing Cotton tensor.

PhysicsWeyl tensorPhysics and Astronomy (miscellaneous)Cotton tensorFOS: Physical sciencesGeneral Relativity and Quantum Cosmology (gr-qc)KinematicsFirst orderObserver (physics)General Relativity and Quantum Cosmologysymbols.namesakeGeneral Relativity and Quantum CosmologysymbolsCovariant transformationDifferential (mathematics)Mathematical physics
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