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.

A Goldberg-Sachs theorem in dimension three

TAGHAVI-CHABERT, Arman
2015-01-01

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.
2015
32
11
115009
115044
http://iopscience.iop.org/0264-9381/32/11/115009/pdf/0264-9381_32_11_115009.pdf
algebraically special spacetimes; congruences of geodesics; Goldberg-Sachs theorem; three-dimensional pseudo-Riemannian geometry; topological massive gravity;
Nurowski, Paweł; Taghavi-Chabert, Arman
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1622929
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