Abstract
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.
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Communicated by James A. Isenberg.
The author is supported in part by the project ANR-12-BS01-004 ‘Geometry and topology of open manifolds’ of the French National Agency for Research.
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Herzlich, M. Computing Asymptotic Invariants with the Ricci Tensor on Asymptotically Flat and Asymptotically Hyperbolic Manifolds. Ann. Henri Poincaré 17, 3605–3617 (2016). https://doi.org/10.1007/s00023-016-0494-5
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DOI: https://doi.org/10.1007/s00023-016-0494-5