Twistor initial data characterisation of pp-waves

Abstract

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 ${\nabla }_A{}^{A^{\prime }}{\bar{\kappa }}_{A^{\prime }}\ne 0$. In this note it is shown that if ${\nabla }_A{}^{A^{\prime }}{\bar{\kappa }}_{A^{\prime }}=0$ 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.

7 pages

References in corpus (2)

• Killing spinor initial data sets
• Approximate twistors and positive mass