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

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.