Twistor initial data characterisation of pp-waves

This note gives a concise derivation of a twistor-initial-data characterisation of pp-wave spacetimes in vacuum. The construction is based on a similar calculation for the Minkowski spacetime in [Class. Quantum Grav. 28 075010]. The key difference is that for the Minkowski spacetime a necessary condition is that ∇AA'κ̄A' ≠ 0. In this note it is shown that if ∇AA'κ̄A'=0 then the development is a pp-wave spacetime. Furthermore, it is shown that such condition propagates off the initial hypersurface, which, in turn, gives a twistor initial data characterisation of pp-waves.