Weakly regular \(T^2\)-symmetric spacetimes. The future causal geometry of Gowdy spacetimes
type: Item
instance of: scholarly article
title: Weakly regular \(T^2\)-symmetric spacetimes. The future causal geometry of Gowdy spacetimes
zbMATH Open document ID: 1331.35341
author: Jacques Smulevici
author: Philippe G. LeFloch
published in: Journal of Differential Equations
publication date: 2015-11-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/1403.6252
review text: The Gowdy spacetimes play a role of an important toy model for dynamical problems of cosmology, including the standard Big Bang model, since they allows an analytical consideration of non-trivial non-stationary phenomena. Here, the authors focus their attention on a global causal structure in the sense of distributions considering global future geometry of spacetimes with general \(T^2\) symmetry within the weak version of the Einstein equations defined geometrically. The principal result of this work, the proof of future timelike geodesically completeness for the weakly regular Gowdy spacetimes, is based on several steps highlighting new features of the model: the correction term controlled by the energy is introduced to obtain new energy functional, avoiding high-order derivatives and pointwise estimates of Christoffel symbols.
Mathematics Subject Classification ID: 35Q76
zbMATH DE Number: 6506394
zbMATH Keywords: Einstein equations
zbMATH Keywords: Gowdy symmetry
zbMATH Keywords: global causal structure
zbMATH Keywords: future geodesic completeness
reviewed by: Eugene Postnikov
MaRDI profile type: Publication
OpenAlex ID: W2963109483
arXiv ID: 1403.6252
cites work: Global foliations of vacuum spacetimes with \(T^2\) isometry
cites work: The formation of trapped surfaces in spherically-symmetric Einstein-Euler spacetimes with bounded variation
cites work: Future global in time Einsteinian spacetimes with \(U(1)\) isometry group
cites work: Bounded variation solutions of the spherically symmetric einstein‐scalar field equations
cites work: Strong cosmic censorship in polarised Gowdy spacetimes
cites work: Vacuum spacetimes with two-parameter spacelike isometry groups and compact invariant hypersurfaces: Topologies and boundary conditions
cites work: Weakly regular Einstein-Euler spacetimes with Gowdy symmetry: the global areal foliation
cites work: On the Area of the Symmetry Orbits in Weakly Regular Einstein--Euler Spacetimes with Gowdy Symmetry
cites work: Asymptotic behaviour of the gravitational field and the nature of singularities in Gowdy spacetimes
cites work: Definition and stability of Lorentzian manifolds with distributional curvature
cites work: A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on \(T ^{3}\)
cites work: Global geometry of \(T^2\)-symmetric spacetimes with weak regularity
cites work: Weakly regular \(T^2\)-symmetric spacetimes. The global geometry of future Cauchy developments
cites work: Future asymptotics and geodesic completeness of polarized T2-symmetric spacetimes
cites work: Shock waves and gravitational waves in matter spacetimes with Gowdy symmetry
cites work: The characteristic initial value problem for plane symmetric spacetimes with weak regularity
cites work: Plane-symmetric spacetimes with positive cosmological constant: the case of stiff fluids
cites work: Shock Waves in Plane Symmetric Spacetimes
cites work: Existence of constant mean curvature foliations in spacetimes with two-dimensional local symmetry
cites work: On a wave map equation arising in general relativity
cites work: Strong cosmic censorship in \(T^3\)-Gowdy spacetimes
cites work: Strong cosmic censorship for \(T ^{2}\)-symmetric spacetimes with cosmological constant and matter
cites work: On the area of the symmetry orbits of cosmological spacetimes with toroidal or hyperbolic symmetry
DOI: 10.1016/J.JDE.2015.09.029
description: scientific article