A Goldberg-Sachs theorem in dimension three

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Authors

NUROWSKI Pawel TAGHAVI-CHABERT Arman

Year of publication 2015
Type Article in Periodical
Magazine / Source Classical and Quantum Gravity
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1088/0264-9381/32/11/115009
Field General mathematics
Keywords three-dimensional pseudo-Riemannian geometry; Goldberg-Sachs theorem; congruences of geodesics; algebraically special spacetimes; topological massive gravity
Description 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 trace-free 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.
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