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Optical (or Robinson) structures are one generalisation of four-dimensionalshearfree congruences of null geodesics to higher dimensions. They areLorentzian analogues of complex and CR structures. In this context, we extendthe Goldberg-Sachs theorem to five dimensions. To be precise, we find a newalgebraic condition on the Weyl tensor, which generalises the Petrov type IIcondition, in the sense that it ensures the existence of such congruences on afive-dimensional spacetime, vacuum or under weaker assumptions on the Riccitensor. This results in a significant simplification of the field equations. Wediscuss possible degenerate cases, including a five-dimensional generalisationof the Petrov type D condition. We also show that the vacuum black ringsolution is endowed with optical structures, yet fails to be algebraicallyspecial with respect to them. We finally explain the generalisation of theseideas to higher dimensions, which has been checked in six and seven dimensions.

Optical structures, algebraically special spacetimes, and the Goldberg-Sachs theorem in five dimensions