A Goldberg-Sachs theorem in dimension three
| Authors | |
|---|---|
| Year of publication | 2015 |
| Type | Article in Periodical |
| Magazine / Source | Classical and Quantum Gravity |
| MU Faculty or unit | |
| 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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