The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions
arXiv:1006.4467 · doi:10.1007/s00023-011-0076-5
Abstract
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.
83 pages, 1 figure