Existence of CMC and Constant Areal Time Foliations inT2Symmetric Spacetimes with Vlasov Matter

DOI10.1081/PDE-120028852zbMath1063.35145arXivgr-qc/0211063MaRDI QIDQ3157892

Alan D. Rendall, M. Weaver, Håakan Andréasson

Publication date: 20 January 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/gr-qc/0211063

zbMATH Keywords

Einstein equationsVlasov equationlong-time existenceconstant mean curvature foliation

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) PDEs in connection with relativity and gravitational theory (35Q75)

Related Items (7)

Areal foliation and asymptotically velocity-term dominated behavior in T2 symmetric space-times with positive cosmological constant ⋮ LOCAL EXISTENCE AND CONTINUATION CRITERIA FOR SOLUTIONS OF THE EINSTEIN–VLASOV-SCALAR FIELD SYSTEM WITH SURFACE SYMMETRY ⋮ A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on \(T ^{3}\) ⋮ The Einstein-Vlasov system/kinetic theory ⋮ Theorems on existence and global dynamics for the Einstein equations ⋮ Proof of the cosmic no-hair conjecture in the \(\mathbb{T}^3\)-Gowdy symmetric Einstein-Vlasov setting ⋮ Static spherically symmetric Einstein-Vlasov bifurcations of the Schwarzschild spacetime

Cites Work

• Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics
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• Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data
• Global existence of solutions of the spherically symmetric Vlasov- Einstein system with small initial data
• Global foliations of vacuum spacetimes with \(T^2\) isometry
• The ``Two and one-half dimensional relativistic Vlasov Maxwell system
• Existence of constant mean curvature foliations in spacetimes with two-dimensional local symmetry
• Global foliations of matter spacetimes with Gowdy symmetry
• Problème de Cauchy pour le système intégro-différentiel d'Einstein-Liouville. (Cauchy problem for the Einstein-Liouville integro-differential system)
• On the ‘one and one-half dimensional’ relativistic Vlasov-Maxwell system
• Existence and non-existence results for global constant mean curvature foliations
• Cosmological spacetimes not covered by a constant mean curvature slicing
• Cosmological solutions of the Vlasov-Einstein system with spherical, plane, and hyperbolic symmetry
• The Large Scale Structure of Space-Time

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