The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions
General Relativity and Quantum Cosmology
2011-07-14 v1
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.
Keywords
Cite
@article{arxiv.1006.4467,
title = {The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions},
author = {Yvonne Choquet-Bruhat and Piotr T. Chruściel and José M. Martín-García},
journal= {arXiv preprint arXiv:1006.4467},
year = {2011}
}
Comments
83 pages, 1 figure