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

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

2010-06-23

arxiv.org/abs/1006.4467v1

Annales Henri Poincare 12:419-482,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

83 pages, 1 figure

Scientific paper

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 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.

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