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

Daniel Maerten
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Abstract

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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Daniel Maerten. 2006-01-24. Positive energy-momentum theorem in asymptotically anti de Sitter space-times. https://arxiv.org/abs/math/0506061

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