A Goldberg-Sachs theorem in dimension three
General Relativity and Quantum Cosmology
2015-05-14 v2 High Energy Physics - Theory
Mathematical Physics
Differential Geometry
math.MP
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.
Keywords
Cite
@article{arxiv.1502.00304,
title = {A Goldberg-Sachs theorem in dimension three},
author = {Pawel Nurowski and Arman Taghavi-Chabert},
journal= {arXiv preprint arXiv:1502.00304},
year = {2015}
}
Comments
31 pages. v2: minor typographic changes in the bibliography