Killing vectors in asymptotically flat space–times. I. Asymptotically translational Killing vectors and the rigid positive energy theorem

DOI10.1063/1.531497zbMath0864.53063arXivgr-qc/9510015OpenAlexW3103619227MaRDI QIDQ5284454

Robert Beig, Piotr T. Chrusciel

Publication date: 17 June 1997

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/gr-qc/9510015

zbMATH Keywords

energy conditionKilling vector fieldsasymptotically flat spacetimepositive energy theoremuniqueness of stationary black holes

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Gravitational energy and conservation laws; groups of motions (83C40)

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Cites Work

• Unnamed Item
• On Witten's proof of the positive energy theorem
• A strictly-positive mass theorem
• On the invariant mass conjecture in general relativity
• The boost problem in general relativity
• Proof of the positive mass theorem. II
• Maximal hypersurfaces in stationary asymptotically flat spacetimes
• A new proof of the positive energy theorem.
• Asymptotic estimates in Weighted Hölder spaces for a class of elliptic scale-covariant second order operators
• The mass of an asymptotically flat manifold
• Isometries compatible with asymptotic flatness at null infinity: A complete description
• Null infinity and Killing fields
• Existence theorem for solutions of Witten’s equation and nonnegativity of total mass
• On completeness of orbits of Killing vector fields
• On the existence of neutrino ’’zero-modes’’ in vacuum spacetimes
• Positivity of mass for certain spacetimes with horizons
• RIEMANNsche Räume mit ebenfrontiger und mit ebener Symmetrie