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

Understand

Optical (or Robinson) structures are one generalisation of four-dimensional shearfree congruences of null geodesics to higher dimensions.

• They are Lorentzian analogues of complex and CR structures.
• In this context, we extend the Goldberg-Sachs theorem to five dimensions.
• To be precise, we find a new algebraic condition on the Weyl tensor, which generalises the Petrov type II condition, in the sense that it ensures the existence of such congruences on a five-dimensional spacetime, vacuum or under weaker assumptions on the Ricci tensor.