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

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.

arXiv comment2005, 35 pages, to appear in Annales Henri Poincaré

Cited by in corpus (3)

• Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space-times
• Killing vectors in asymptotically flat space--times: II. Asymptotically translational Killing vectors and the rigid positive energy theorem in higher dimensions
• The hyperbolic positive energy theorem