Localizing solutions of the Einstein constraint equations

DOI10.1007/s00222-015-0642-4zbMath1353.83010arXiv1407.4766OpenAlexW2962917555MaRDI QIDQ328869

Alessandro Carlotto, Richard M. Schoen

Publication date: 21 October 2016

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.4766

zbMATH Keywords

black holeEarthstrong gravitational fieldsastrophysical anomaliesgravitational shieldingMilky WayPicard iteration scheme

Mathematics Subject Classification ID

Black holes (83C57) Applications of differential geometry to physics (53Z05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Galactic and stellar structure (85A15) Exact solutions to problems in general relativity and gravitational theory (83C15) Approximation procedures, weak fields in general relativity and gravitational theory (83C25)

Related Items (31)

The general relativistic constraint equations ⋮ Rigidity of stable minimal hypersurfaces in asymptotically flat spaces ⋮ Gauge-invariant observables, gravitational dressings, and holography in AdS ⋮ Rigidity of stable marginally outer trapped surfaces in initial data sets ⋮ On Carlotto-Schoen-type scalar-curvature gluings ⋮ BMS charges without supertranslation ambiguity ⋮ Stability of Minkowski space and polyhomogeneity of the metric ⋮ Rigidity of Hawking mass for surfaces in three manifolds ⋮ Density and positive mass theorems for initial data sets with boundary ⋮ Metrics with \(\lambda_1(-\Delta + k R) \ge 0\) and flexibility in the Riemannian Penrose inequality ⋮ Hyperbolic mass via horospheres ⋮ Constrained deformations of positive scalar curvature metrics, II ⋮ Gluing for the constraints for higher spin fields ⋮ Doubling of asymptotically flat half-spaces and the Riemannian Penrose inequality ⋮ The seed-to-solution method for the Einstein constraints and the asymptotic localization problem ⋮ Recent progress in general relativity ⋮ Multi-localized time-symmetric initial data for the Einstein vacuum equations ⋮ Mathematical aspects of general relativity. Abstracts from the workshop held August 29 -- September 4, 2021 (hybrid meeting) ⋮ Numerical initial data deformation exploiting a gluing construction: I. Exterior asymptotic Schwarzschild ⋮ Black hole gluing in de Sitter space ⋮ Global solvability of the vacuum Einstein equation and the strong cosmic censorship in four dimensions ⋮ Relative volume comparison for asymptotically flat manifolds and rigidity of total mass ⋮ A survey on positive scalar curvature metrics ⋮ Evaluation of the ADM mass and center of mass via the Ricci tensor ⋮ Asymptotically flat three-manifolds contain minimal planes ⋮ Effective versions of the positive mass theorem ⋮ Global regularity of solutions of the Einstein-Klein-Gordon system: A review ⋮ Lower semicontinuity of the ADM mass in dimensions two through seven ⋮ Global uniqueness of large stable CMC spheres in asymptotically flat Riemannian \(3\)-manifolds ⋮ Positive energy theorems in fourth-order gravity ⋮ A positive energy theorem for fourth-order gravity

Cites Work

• Unnamed Item
• Rigidity of stable marginally outer trapped surfaces in initial data sets
• Rigidity of area-minimizing hyperbolic surfaces in three-manifolds
• Construction of \(N\)-body initial data sets in general relativity
• Rigidity of area-minimizing two-spheres in three-manifolds
• Large-sphere and small-sphere limits of the Brown-York mass
• Deformations of the scalar curvature
• On the proof of the positive mass conjecture in general relativity
• A new proof of the positive energy theorem.
• Rigidity of area-minimizing free boundary surfaces in mean convex three-manifolds
• On the asymptotics for the vacuum Einstein constraint equations
• Initial data engineering
• Rigidity of stable minimal hypersurfaces in asymptotically flat spaces
• The spacetime positive mass theorem in dimensions less than eight
• Interior estimates for elliptic systems of partial differential equations
• The mass of an asymptotically flat manifold
• On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications
• Linearization stability of the Einstein equations
• Splitting of 3-manifolds and rigidity of area-minimising surfaces
• Scalar curvature deformation and a gluing construction for the Einstein constraint equations

This page was built for publication: Localizing solutions of the Einstein constraint equations