Universal Positive Mass Theorems

In this paper, we develop a general study of contributions at infinity of Bochner–Weitzenböck-type formulas on asymptotically flat manifolds, inspired by Witten’s proof of the positive mass theorem. As an application, we show that similar proofs can be obtained in a much more general setting as any...

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Bibliographic Details
Published in:Communications in mathematical physics 2017-05, Vol.351 (3), p.973-992
Main Author: Herzlich, Marc
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Curvature
Differential Geometry
Infinity
Mathematical and Computational Physics
Mathematical Physics
Mathematics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theorems
Theoretical
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Summary:In this paper, we develop a general study of contributions at infinity of Bochner–Weitzenböck-type formulas on asymptotically flat manifolds, inspired by Witten’s proof of the positive mass theorem. As an application, we show that similar proofs can be obtained in a much more general setting as any choice of an irreducible natural bundle and a very large choice of first-order operators may lead to a positive mass theorem along the same lines if the necessary curvature conditions are satisfied.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-016-2777-6