Computing asymptotic invariants with the Ricci tensor on asymptotically flat and hyperbolic manifolds

We prove in a simple and coordinate-free way the equivalence bteween the classical definitions of the mass or 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 stat...

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Bibliographic Details
Published in:arXiv.org 2016-04
Main Author: Herzlich, Marc
Format: Article
Language:English
Subjects:
Asymptotic properties
Manifolds
Mathematical analysis
Tensors
Online Access:Get full text
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Summary:We prove in a simple and coordinate-free way the equivalence bteween the classical definitions of the mass or 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:2331-8422
DOI:10.48550/arxiv.1503.00508