The Cauchy Problem on a Characteristic Cone for the Einstein Equations in Arbitrary Dimensions

作者：Choquet Bruhat Yvonne^*; Chrusciel Piotr T; Martin Garcia Jose M

来源：Annales Henri Poincare, 2011, 12(3): 419-482.

DOI：10.1007/s00023-011-0076-5

We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary space-time dimensions n + 1 a parts per thousand yen 3. 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.

• 出版日期2011-4