Computing Asymptotic Invariants with the Ricci Tensor on Asymptotically Flat and Asymptotically Hyperbolic Manifolds

We prove in a simple and coordinate-free way the equivalence between the classical definitions of the mass or of the center of mass of an asymptotically flat manifold and their alternative definitions depending on the Ricci tensor and conformal Killing fields. This enables us to prove an analogous s...

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Bibliographic Details
Published in:Annales Henri Poincaré 2016-12, Vol.17 (12), p.3605-3617
Main Author: Herzlich, Marc
Format: Article
Language:English
Subjects:
Asymptotic properties
Classical and Quantum Gravitation
Dynamical Systems and Ergodic Theory
Elementary Particles
Manifolds
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity Theory
Theoretical
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Summary:We prove in a simple and coordinate-free way the equivalence between the classical definitions of the mass or of the center of mass of an asymptotically flat manifold and their alternative definitions depending on the Ricci tensor and conformal Killing fields. This enables us to prove an analogous statement in the asymptotically hyperbolic case.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-016-0494-5