Revisiting the characteristic initial value problem for the vacuum Einstein field equations

Understand

Using the Newman-Penrose formalism we study the characteristic initial value problem in vacuum General Relativity.

• We work in a gauge suggested by Stewart, and following the strategy taken in the work of Luk, demonstrate local existence of solutions in a neighbourhood of the set on which data are given.
• These data are given on intersecting null hypersurfaces.
• Existence near their intersection is achieved by combining the observation that the field equations are symmetric hyperbolic in this gauge with the results of Rendall.