A Goldberg-Sachs theorem in dimension three

Abstract

We prove a Goldberg-Sachs theorem in dimension three. To be precise, given a three-dimensional Lorentzian manifold satisfying the topological massive gravity equations, we provide necessary and sufficient conditions on the tracefree Ricci tensor for the existence of a null line distribution whose orthogonal complement is integrable and totally geodetic. This includes, in particular, Kundt spacetimes that are solutions of the topological massive gravity equations.

31 pages. v2: minor typographic changes in the bibliography

References in corpus (6)

• Classification of the Weyl Tensor in Higher Dimensions
• Killing-Yano tensors and multi-hermitian structures
• On a five-dimensional version of the Goldberg-Sachs theorem
• The complex Goldberg-Sachs theorem in higher dimensions
• Three-dimensional spacetimes of maximal order
• Optical structures, algebraically special spacetimes, and the Goldberg-Sachs theorem in five dimensions

Cited by in corpus (7)

• Kerr-Schild Double Copy and Complex Worldlines
• Kundt solutions of Minimal Massive 3D Gravity
• Pure spinors, intrinsic torsion and curvature in odd dimensions
• On geometry of congruences of null strings in 4-dimensional complex and real pseudo-Riemannian spaces
• Gravitational Waves from Thurston Geometries
• Almost Robinson geometries
• Impulsive gravitational waves in general massive 3D gravity