Global existence of solutions of the spherically symmetric Vlasov- Einstein system with small initial data

DOI10.1007/BF02096962zbMath0774.53056OpenAlexW2034172803WikidataQ95001961 ScholiaQ95001961MaRDI QIDQ1208013

Gerhard Rein, Alan D. Rendall

Publication date: 16 May 1993

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02096962

zbMATH Keywords

cosmic censorshipEinstein equationsspherically symmetric solutionsVlasov equations

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Propagation of singularities; initial value problems on manifolds (58J47)

Related Items

The nonvacuum Einstein flow on surfaces of negative curvature and nonlinear stability ⋮ The Newtonian limit for asymptotically flat solutions of the Vlasov- Einstein system ⋮ Existence of CMC and Constant Areal Time Foliations inT²Symmetric Spacetimes with Vlasov Matter ⋮ On the Jeans theorem and the ``Tolman-Oppenheimer-Volkoff equation in \(R^2\) gravity ⋮ Global existence of classical solutions to the Vlasov-Poisson system in a three-dimensional, cosmological setting ⋮ The entropy conservation and energy conservation for the relativistic Vlasov-Klein-Gordon system ⋮ A regularity theorem for solutions of the spherically symmetric Vlasov- Einstein system ⋮ Gravitational collapse and the formation of black holes for the spherically symmetric Einstein-Vlasov system ⋮ Derivation of the equations of electrodynamics and gravity from the principle of least action ⋮ The Einstein-Vlasov system in maximal areal coordinates-local existence and continuation ⋮ Small data solutions of the Vlasov-Poisson system and the vector field method ⋮ The global nonlinear stability of Minkowski space for the massless Einstein-Vlasov system ⋮ A vector field method for relativistic transport equations with applications ⋮ Existence of initial data satisfying the constraints for the spherically symmetric Einstein–Vlasov–Maxwell system ⋮ On derivation of equations of electrodynamics and gravitation from the principle of least action, the Hamilton-Jacobi method, and cosmological solutions ⋮ Global classical solutions to the 3D Nordström-Vlasov system ⋮ Static solutions of the spherically symmetric Vlasov–Einstein system ⋮ Black Hole Formation from a Complete Past for the Einstein–Vlasov System ⋮ The relativistic Boltzmann equation on a spherically symmetric gravitational field ⋮ The constraint equations of the Einstein-Vlasov-Maxwell system in the maximal-isotropic coordinates ⋮ Black hole formation from a complete regular past for collisionless matter ⋮ Future stability of expanding spatially homogeneous FLRW solutions of the spherically symmetric Einstein–massless Vlasov system with spatial topology R3 ⋮ Regularity results for the spherically symmetric Einstein-Vlasov system ⋮ On the small redshift limit of steady states of the spherically symmetric Einstein–Vlasov system and their stability ⋮ Existence globale de solutions au système sphériquement symétrique de Einstein-Vlasov-Maxwell ⋮ A proof of the instability of AdS for the Einstein-massless Vlasov system ⋮ On derivation of equations of gravitation from the principle of least action, relativistic Milne-McCrea solutions, and Lagrange points ⋮ Global existence of solutions to the spherically symmetric Einstein-Vlasov-Maxwell system ⋮ The formation of black holes in spherically symmetric gravitational collapse ⋮ Global Existence for the Spherically Symmetric Einstein–Vlasov System with Outgoing Matter ⋮ Global existence of smooth solutions for three-dimensional magnetic Bénard system with mixed partial dissipation, magnetic diffusion and thermal diffusivity ⋮ Cosmological solutions of the Vlasov-Einstein system with spherical, plane, and hyperbolic symmetry ⋮ The fractional kinetic Einstein-Vlasov system and its implications in Bianchi spacetimes geometry ⋮ Mini-workshop: Relativistic fluids at the intersection of mathematics and physics. Abstracts from the mini-workshop held December 13--19, 2020 (online meeting) ⋮ Stability for the spherically symmetric Einstein–Vlasov system–a coercivity estimate ⋮ Generalized solutions of the Vlasov-Poisson system with singular data ⋮ Models for self-gravitating photon shells and geons ⋮ A numerical stability analysis for the Einstein–Vlasov system ⋮ Dynamics of gravitational collapse in the axisymmetric Einstein–Vlasov system ⋮ Rotating, stationary, axially symmetric spacetimes with collisionless matter ⋮ The asymptotic behaviour in Schwarzschild time of Vlasov matter in spherically symmetric gravitational collapse ⋮ The Newtonian limit of the spherically symmetric Vlasov-Einstein system ⋮ A class of dust-like self-similar solutions of the massless Einstein-Vlasov system ⋮ Theorems on existence and global dynamics for the Einstein equations ⋮ Classical solutions to the Vlasov-Poisson system in an accelerating cosmological setting ⋮ Local and global existence theorems for the Einstein equations ⋮ Optimal gradient estimates and asymptotic behaviour for the Vlasov-Poisson system with small initial data ⋮ The Einstein-Vlasov system/kinetic theory ⋮ Theorems on existence and global dynamics for the Einstein equations ⋮ Stable self-similar blow up dynamics for the three dimensional relativistic gravitational Vlasov-Poisson system ⋮ Unnamed Item ⋮ FORMATION OF TRAPPED SURFACES FOR THE SPHERICALLY SYMMETRIC EINSTEIN–VLASOV SYSTEM ⋮ Strong Cosmic Censorship for Surface-Symmetric Cosmological Spacetimes with Collisionless Matter ⋮ Global weak solutions to the relativistic BGK equation ⋮ The stability of the Minkowski space for the Einstein-Vlasov system ⋮ The Vlasov limit for a system of particles which interact with a wave field ⋮ The stability of the Minkowski space for the Einstein-Vlasov system ⋮ Static spherically symmetric Einstein-Vlasov bifurcations of the Schwarzschild spacetime ⋮ Global stability of Minkowski space for the Einstein-Vlasov system in the harmonic gauge ⋮ On Classical Solutions of the Nordström-Vlasov System ⋮ Asymptotic stability of Minkowski space-time with non-compactly supported massless Vlasov matter ⋮ Vector field methods for kinetic equations with applications to classical and relativistic systems ⋮ Black hole formation from a complete regular past ⋮ Existence of Static Solutions of the Einstein--Vlasov--Maxwell System and the Thin Shell Limit ⋮ Propagation of regularity and long time behavior of the \(3D\) Massive relativistic transport equation. II: Vlasov-Maxwell system ⋮ On the Cylindrically Symmetric Einstein–Vlasov System ⋮ Nonlinear stability of the Milne model with matter ⋮ The Cauchy Problem for the Einstein–Vlasov System ⋮ A NOTE ON THE COLLAPSE OF SMALL DATA SELF-GRAVITATING MASSLESS COLLISIONLESS MATTER ⋮ COSMOLOGY OF EINSTEIN–VLASOV SYSTEM IN A WEAK MODIFICATION OF GENERAL RELATIVITY ⋮ Static Solutions to the Einstein--Vlasov System with a Nonvanishing Cosmological Constant

Cites Work

• Unnamed Item
• Unnamed Item
• Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics
• Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data
• Singularity formation in a collisionless plasma could occur only at high velocities
• Formation of singularities in three-dimensional compressible fluids
• The problem of a self-gravitating scalar field
• Propagation of moments and regularity for the 3-dimensional Vlasov- Poisson system
• Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data
• The Newtonian limit of the spherically symmetric Vlasov-Einstein system
• Global symmetric solutions of the initial value problem of stellar dynamics
• Global existence of generalized solutions of the spherically symmetric Einstein-scalar equations in the large
• The structure and uniqueness of generalized solutions of the spherically symmetric Einstein-scalar equations
• A mathematical theory of gravitational collapse
• Problème de Cauchy pour le système intégro-différentiel d'Einstein-Liouville. (Cauchy problem for the Einstein-Liouville integro-differential system)
• The formation of black holes and singularities in spherically symmetric gravitational collapse
• Global existence of smooth solutions to the vlasov poisson system in three dimensions
• The initial value problem for a class of general relativistic fluid bodies
• Bounded variation solutions of the spherically symmetric einstein‐scalar field equations
• The Large Scale Structure of Space-Time
• On Continued Gravitational Contraction