A Goldberg-Sachs theorem in dimension three

• Autoři: NUROWSKI Pawel; TAGHAVI-CHABERT Arman
• Rok publikování: 2015
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Classical and Quantum Gravity
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• Doi: http://dx.doi.org/10.1088/0264-9381/32/11/115009
• Obor: Obecná matematika
• Klíčová slova: three-dimensional pseudo-Riemannian geometry; Goldberg-Sachs theorem; congruences of geodesics; algebraically special spacetimes; topological massive gravity
• Popis: 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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