The ADM mass of asymptotically flat hypersurfaces
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- by Levi Lopes de Lima and Frederico Girão PDF
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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.References
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Additional Information
- Levi Lopes de Lima
- Affiliation: Department of Mathematics, Federal University of Ceará, Campus do Pici, Av. Humberto Monte, s/n, 60455-760, Fortaleza/CE, Brazil
- Email: levi@mat.ufc.br
- Frederico Girão
- Affiliation: Department of Mathematics, Federal University of Ceará, Campus do Pici, Av. Humberto Monte, s/n, 60455-760, Fortaleza/CE, Brazil
- ORCID: 0000-0002-4418-2737
- Email: fred@mat.ufc.br
- Received by editor(s): March 10, 2012
- Received by editor(s) in revised form: June 8, 2013
- Published electronically: October 3, 2014
- Additional Notes: This work was partially supported by CNPq/BR and FUNCAP/CE
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 367 (2015), 6247-6266
- MSC (2010): Primary 53C21; Secondary 53C80
- DOI: https://doi.org/10.1090/S0002-9947-2014-05902-3
- MathSciNet review: 3356936