A Goldberg-Sachs theorem in dimension three
arXiv:1502.00304 · doi:10.1088/0264-9381/32/11/115009
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