On maximal globally hyperbolic vacuum space-times
General Relativity and Quantum Cosmology
2013-10-11 v2
Authors:
Piotr T. Chruściel
Abstract
We prove existence and uniqueness of maximal global hyperbolic developments of vacuum general relativistic initial data sets with initial data (g,K) in Sobolev spaces Hs⊕Hs−1 with integer s > n/2 +1.
Cite
@article{arxiv.1112.5779,
title = {On maximal globally hyperbolic vacuum space-times},
author = {Piotr T. Chruściel},
journal= {arXiv preprint arXiv:1112.5779},
year = {2013}
}
Comments
various improvements
Related papers
View all related →
Analysis of PDEs · Mathematics
Hyperbolic Problems in the Whole Scale of Sobolev-Type Spaces of Periodic Functions
Irina Kmit
2025-12-10
General Relativity and Quantum Cosmology · Physics
On the area of the symmetry orbits of cosmological spacetimes with toroidal or hyperbolic symmetry
Jacques Smulevici
2009-04-07
Analysis of PDEs · Mathematics
Sharp k-order Sobolev inequalities in the hyperbolic space ${\Bbb H}^n$
Genqian Liu
2013-10-01
Mathematical Physics · Physics
Diagonal hyperbolic systems with large and monotone data Part I: Global continuous solutions
Ahmad El Hajj, Régis Monneau
2009-04-14
Analysis of PDEs · Mathematics
Existence of global solutions to the Fokas-Lenells equation with arbitrary spectral singularities
Yuan Li, Qiaoyuan Cheng, Engui Fan
2025-12-29
Analysis of PDEs · Mathematics
Global solutions to the Kirchhoff equation with spectral gap data in the energy space
Marina Ghisi, Massimo Gobbino
2022-08-11
Differential Geometry · Mathematics
On complete maximal submanifolds in pseudo-hyperbolic space
Andrea Seppi, Graham Smith, Jérémy Toulisse
2023-05-25
General Relativity and Quantum Cosmology · Physics
Hyperbolic Mass in 2+1 Dimensions
Raphaela Wutte
2025-09-03
Mathematical Physics · Physics
Global continuous solutions to diagonalizable hyperbolic systems with large and monotone data
Ahmad El Hajj, Regis Monneau
2008-12-18
Analysis of PDEs · Mathematics
Global well-posedness in Sobolev space implies global existence for weighted L^2 initial data for L^2 -critical NLS
P. Blue, J. Colliander
2010-01-09
Analysis of PDEs · Mathematics
Solution of second-order hyperbolic quasilinear systems with spatio-characteristic initial data in weighted Sobolev-type spaces under finite differentiability assumptions on the data
Louokdom Tamto Paul Giscard, Duplex Elvis Houpa Danga, Kouakep Tchaptchie Yannick
2026-05-06
Analysis of PDEs · Mathematics
Local and global well-posedness of wave maps on $\R^{1+1}$ for rough data
Marcus Keel, Terence Tao
2009-07-14
Analysis of PDEs · Mathematics
Nonuniform dependence on initial data for compressible gas dynamics: The periodic Cauchy problem
Barbara Lee Keyfitz, Feride Tiglay
2016-11-18
Differential Geometry · Mathematics
A closure result for globally hyperbolic spacetimes
Giovanni Catino, Alberto Roncoroni
2024-09-12
Analysis of PDEs · Mathematics
On the sharp regularity of solutions to hyperbolic boundary value problems
Corentin Audiard
2022-06-28
Analysis of PDEs · Mathematics
Global dynamics of a supercritical wave equation in a large data regime
Shijie Dong, Zoe Wyatt, Jingya Zhao
2026-05-18
Differential Geometry · Mathematics
Enveloping space of a globally hyperbolic conformally flat spacetime
Rym Smaï
2023-11-30
General Relativity and Quantum Cosmology · Physics
Sobolev spaces for multi-black hole initial data
María E. Gabach-Clément, Andrés Aceña
2019-06-07
General Relativity and Quantum Cosmology · Physics
Gluing Initial Data Sets for General Relativity
Piotr T. Chrusciel, James Isenberg, Daniel Pollack
2007-05-23
General Relativity and Quantum Cosmology · Physics
The maximal existence region of the analytic solutions for a class of characteristic Einstein vacuum equations
G. Caciotta, F. Nicolò
2018-11-14
Functional Analysis · Mathematics
Characterizations for the existence of traces of first-order Sobolev spaces on hyperbolic fillings
Manzi Huang, Zhihao Xu
2022-05-03
Analysis of PDEs · Mathematics
Lagrangian Averaged Navier-Stokes equations with rough data in Sobolev space
Nathan Pennington
2011-08-08
Analysis of PDEs · Mathematics
The unique limit of the Glimm-Lax construction for Sobolev data and obstructions to 1-d convex integration
Jeffrey Cheng, Cooper Faile, Sam G. Krupa
2026-01-06
General Relativity and Quantum Cosmology · Physics
Hyperbolic Formulation of General Relativity
Andrew Abrahams, Arlen Anderson, Yvonne Choquet-Bruhat, James W. York,
2012-08-27
General Relativity and Quantum Cosmology · Physics
On future geodesic completeness for the Einstein-Vlasov system with hyperbolic symmetry
Gerhard Rein
2007-05-23