The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions

Understand

We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary dimensions.

• We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime solution of the Cauchy problem on a characteristic cone for the hyperbolic system of the reduced Einstein equations in wave-map gauge also satisfies the full Einstein equations.
• We prove a geometric uniqueness theorem for this Cauchy problem in the vacuum case.