A Goldberg–Sachs theorem in dimension three. (12th May 2015)

• Record Type: Journal Article
• Authors: Nurowski, Paweł; Taghavi-Chabert, Arman
• Is Part Of: Classical and quantum gravity. Volume 32:Number 11(2015:Jun.)
• Publication Date: 2015-05-12
• Subjects: three-dimensional pseudo-Riemannian geometry -- Goldberg–Sachs theorem -- congruences of geodesics -- algebraically special spacetimes -- topological massive gravity; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/0264-9381/32/11/115009
• Languages: English
• ISSNs: 0264-9381

Abstract

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.