Abstract.
The aim of this paper is to prove a positive energy-momentum theorem under the (well known in general relativity) dominant energy condition, for AdS-asymptotically hyperbolic manifolds. These manifolds are by definition endowed with a Riemannian metric and a symmetric 2-tensor which respectively tend to the metric and second fundamental form of a standard hyperbolic slice in Anti-de Sitter space-time. There exists a positive mass theorem for asymptotically hyperbolic spin Riemannian manifolds (with zero extrinsic curvature), and we present an extension of this result for the non zero extrinsic curvature case.
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Communicated by Sergiu Klainerman
Submitted: January 15, 2006 Accepted: January 15, 2006
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Maerten, D. Positive Energy-Momentum Theorem for AdS-Asymptotically Hyperbolic Manifolds. Ann. Henri Poincaré 7, 975–1011 (2006). https://doi.org/10.1007/s00023-006-0273-9
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DOI: https://doi.org/10.1007/s00023-006-0273-9