The ADM mass of asymptotically flat hypersurfaces

de Lima, Levi; Girão, Frederico

doi:10.1090/S0002-9947-2014-05902-3

The ADM mass of asymptotically flat hypersurfaces
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by Levi Lopes de Lima and Frederico Girão PDF

Trans. Amer. Math. Soc. 367 (2015), 6247-6266 Request permission

Abstract:

We provide integral formulae for the ADM mass of asymptotically flat hypersurfaces in Riemannian manifolds with a certain warped product structure in a neighborhood of ‘spatial’ infinity, thus extending Lam’s recent results on Euclidean graphs to this broader context. As applications we exhibit, in any dimension, new examples of manifolds for which versions of the Positive Mass and Riemannian Penrose inequalities hold and discuss a notion of quasi-local mass in this setting. The proof explores a novel connection between the co-vector defining the ADM mass of a hypersurface as above and the Newton tensor associated to its shape operator, which takes place in the presence of an ambient Killing field.

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