Positive energy-momentum theorem in asymptotically anti de Sitter space-times

Details Positive energy-momentum theorem in asymptotically anti de Sitter space-times Positive energy-momentum theorem in asymptotically anti de Sitter space-times

2005-06-03

arxiv.org/abs/math/0506061v3

Mathematics

Differential Geometry

2005, 35 pages, to appear in Annales Henri Poincar\'{e}

Scientific paper

This paper proves a positive energy-momentum theorem for oriented Riemannian 3-manifolds that are asymptotic to a standard hyperbolic slice in anti de Sitter space-time. Analogously to the original Witten's proof in the asymptotically flat case, this result relies on spinorial methods. We also give a rigidity theorem: if the energy-momentum is degenerate (in a certain sense) then our 3-manifold can be isometrically embedded in anti de Sitter.

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