The spacetime positive mass theorem in dimensions less than eight

DOI10.4171/JEMS/584zbMath1341.53067arXiv1110.2087MaRDI QIDQ2633996

Dan A. Lee, Michael Eichmair, Lan-Hsuan Huang, Richard M. Schoen

Publication date: 5 February 2016

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.2087

zbMATH Keywords

positive mass theoremmarginally outer trapped surfaces

Mathematics Subject Classification ID

General relativity (83C99) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (32)

The general relativistic constraint equations ⋮ Total mean curvature of the boundary and nonnegative scalar curvature fill-ins ⋮ Scalar curvature deformation and mass rigidity for ALH manifolds with boundary ⋮ Rigidity of stable minimal hypersurfaces in asymptotically flat spaces ⋮ Yamabe flow and ADM mass on asymptotically flat manifolds ⋮ Book review of: D. A. Lee, Geometric relativity ⋮ Localizing solutions of the Einstein constraint equations ⋮ Rigidity of stable marginally outer trapped surfaces in initial data sets ⋮ Some conformal positive mass theorems ⋮ Equality in the spacetime positive mass theorem ⋮ Density and positive mass theorems for initial data sets with boundary ⋮ Density and positive mass theorems for incomplete manifolds ⋮ Analysis, geometry and topology of positive scalar curvature metrics. Abstracts from the workshop held June 27 -- July 3, 2021 (hybrid meeting) ⋮ Mathematical aspects of general relativity. Abstracts from the workshop held August 29 -- September 4, 2021 (hybrid meeting) ⋮ The Jang equation reduction of the spacetime positive energy theorem in dimensions less than eight ⋮ Positivity of mass in higher dimensions ⋮ On the NNSC fill-ins and asymptotically flat extension ⋮ Positive energy theorem for (4+1)-dimensional asymptotically anti-de Sitter spacetimes ⋮ 4-Dimensional manifolds with nonnegative scalar curvature and CMC boundary ⋮ A note on the positive mass theorem with boundary ⋮ Stability of the spacetime positive mass theorem in spherical symmetry ⋮ Recent progress on the positive energy theorem ⋮ Initial data rigidity results ⋮ Localized deformation for initial data sets with the dominant energy condition ⋮ The Jang equation and the positive mass theorem in the asymptotically hyperbolic setting ⋮ Stable surfaces and free boundary marginally outer trapped surfaces ⋮ Black holes in Einstein–Maxwell theory ⋮ A compactness theorem on Branson's \(Q\)-curvature equation ⋮ From bending of light to positive mass: A non-PDE perspective ⋮ Spacetime harmonic functions and the mass of 3-dimensional asymptotically flat initial data for the Einstein equations ⋮ The case of equality for the spacetime positive mass theorem ⋮ Positive energy theorems in fourth-order gravity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Jenkins-Serrin-type results for the Jang equation
• Existence, regularity, and properties of generalized apparent horizons
• On Witten's proof of the positive energy theorem
• Positive scalar curvature in dim \(\geq 8\)
• A generalization of Hawking's black hole topology theorem to higher dimensions
• Rigidity of marginally trapped surfaces and the topology of black holes
• The area of horizons and the trapped region
• Uniqueness, symmetry, and embeddedness of minimal surfaces
• The boost problem in general relativity
• Proof of the positive mass theorem. II
• Existence of smooth embedded surfaces of prescribed genus that minimize parametric even elliptic functionals on 3-manifolds
• On the first variation of a varifold: Boundary behavior
• The structure of singularities in solutions to ellipsoidal variational problems with constraints in \(R^3\)
• On the proof of the positive mass conjecture in general relativity
• \(\lambda\) minimizing currents
• A new proof of the positive energy theorem.
• The Jang equation reduction of the spacetime positive energy theorem in dimensions less than eight
• The energy and the linear momentum of space-times in general relativity
• The Plateau problem for marginally outer trapped surfaces
• On the asymptotics for the vacuum Einstein constraint equations
• Some uniqueness results for dynamical horizons
• On the center of mass in general relativity
• Complete manifolds with nonnegative scalar curvature and the positive action conjecture in general relativity
• Killing vectors in asymptotically flat space-times. II. Asymptotically translational Killing vectors and the rigid positive energy theorem in higher dimensions
• Some remarks on the size of bodies and black holes
• Positive mass theorems for higher dimensional Lorentzian manifolds
• The mass of an asymptotically flat manifold
• Linearization stability of the Einstein equations
• Killing vectors in asymptotically flat space–times. I. Asymptotically translational Killing vectors and the rigid positive energy theorem

This page was built for publication: The spacetime positive mass theorem in dimensions less than eight