The Cauchy Problem on a Characteristic Cone for the Einstein Equations in Arbitrary Dimensions
- Author(s)
- Yvonne Choquet-Bruhat, Piotr T. Chrusciel, José M. Martin-Garcia
- Abstract
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.
- Organisation(s)
- Gravitational Physics
- External organisation(s)
- Université de recherche Paris Sciences et Lettres, Académie des Sciences
- Journal
- Annales Henri Poincare
- Volume
- 12
- Pages
- 419-482
- No. of pages
- 64
- ISSN
- 1424-0637
- DOI
- https://doi.org/10.1007/s00023-011-0076-5
- Publication date
- 2011
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103036 Theoretical physics, 103028 Theory of relativity, 103019 Mathematical physics
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/the-cauchy-problem-on-a-characteristic-cone-for-the-einstein-equations-in-arbitrary-dimensions(ca765424-7663-4640-a1d4-202ef4e6696a).html