The Mass according to Arnowitt, Deser and Misner

Thierry Aubin

doi:10.1016/j.crma.2007.06.004

Differential Geometry

The Mass according to Arnowitt, Deser and Misner

Presented by: Thierry Aubin

Thierry Aubin ¹

¹ Université Pierre et Marie Curie, 4, place Jussieu, 75252 Paris cedex 05, France

Comptes Rendus. Mathématique, Volume 345 (2007) no. 2, pp. 87-91.

Abstract
Résumé

For asymptotically Euclidean manifolds of order $τ > (n - 2) / 2$ , under the hypothesis that the mass m (according to Arnowitt, Deser and Misner) exists (in particular if the scalar curvature is ⩾0 and integrable), there exists a real number $A > 0$ such that $m ⩾ 4 (n - 1) A$ on each end (except if the metric is Euclidean).

Pour une variété asymptotiquement euclidienne d'ordre $τ > (n - 2) / 2$ , sous l'hypothèse que la masse m (selon Arnowitt, Deser et Misner) existe (notamment si la courbure scalaire est ⩾0 et intégrable), il existe un réel $A > 0$ tel que $m > 4 (n - 1) A$ sur chaque bout (sauf si la métrique est euclidienne).

Received: 2007-03-19
Accepted: 2007-04-27
Published online: 2007-07-15

DOI: 10.1016/j.crma.2007.06.004

Author's affiliations:

Thierry Aubin ¹

¹ Université Pierre et Marie Curie, 4, place Jussieu, 75252 Paris cedex 05, France

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Thierry Aubin. The Mass according to Arnowitt, Deser and Misner. Comptes Rendus. Mathématique, Volume 345 (2007) no. 2, pp. 87-91. doi : 10.1016/j.crma.2007.06.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.06.004/

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