The Einstein-Weyl Equations, Scattering Maps, and Holomorphic Disks
  We show that conformally compact, globally hyperbolic, Lorentzian Einstein-Weyl 3-manifolds are in natural one-to-one correspondence with orientation-reversing diffeomorphisms of the 2-sphere. The proof hinges on a holomorphic-disk analog of Hitchin's mini-twistor correspondence. 
Claude LeBrun and L.J. Mason