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A Definition of Total Energy-Momenta and the Positive Mass Theorem on Asymptotically Hyperbolic 3-Manifolds. I

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Abstract

Two sets of asymptotically hyperbolic initial data are defined, which correspond to the spatial infinity in asymptotically AdS spacetimes and to the null infinity in asymptotically Minkowski spacetimes respectively. The positive mass theorem involving the total energy, the total linear momentum and the total angular momentum is established for these initial data sets.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, P.R. China

    Xiao Zhang

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  1. Xiao Zhang
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Correspondence to Xiao Zhang.

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Communicated by G.W. Gibbons

Research partially supported by National Natural Science Foundation of China under grant 10231050 and the innovation project of the Chinese Academy of Sciences.

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Zhang, X. A Definition of Total Energy-Momenta and the Positive Mass Theorem on Asymptotically Hyperbolic 3-Manifolds. I. Commun. Math. Phys. 249, 529–548 (2004). https://doi.org/10.1007/s00220-004-1056-0

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