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

Autor(en)

Yvonne Choquet-Bruhat, Piotr T. Chrusciel, José M. Martin-Garcia

Abstrakt

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(en)

Gravitationsphysik

Externe Organisation(en)

Université de recherche Paris Sciences et Lettres, Académie des Sciences

Journal

Annales Henri Poincare

Band

12

Seiten

419-482

Anzahl der Seiten

64

ISSN

1424-0637

DOI

https://doi.org/10.1007/s00023-011-0076-5

Publikationsdatum

2011

Peer-reviewed

Ja

ÖFOS 2012

103036 Theoretische Physik, 103028 Relativitätstheorie, 103019 Mathematische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/ca765424-7663-4640-a1d4-202ef4e6696a