On the area of the symmetry orbits in $T^2$ symmetric spacetimes with Vlasov matter

Abstract

This paper treats the global existence question for a collection of general relativistic collisionless particles, all having the same mass. The spacetimes considered are globally hyperbolic, with Cauchy surface a 3-torus. Furthermore, the spacetimes considered are isometrically invariant under a two-dimensional group action, the orbits of which are spacelike 2-tori. It is known from previous work that the area of the group orbits serves as a global time coordinate. In the present work it is shown that the area takes on all positive values in the maximal Cauchy development.

arXiv comment27 pages, version 2 minor changes and corrections

References in corpus (4)

• Global Foliations of Vacuum Spacetimes with $T^2$ Isometry
• Global foliations of matter spacetimes with Gowdy symmetry
• On the area of the symmetry orbits in $T^2$ symmetric spacetimes
• On the existence of global solutions for $T^3$-Gowdy spacetimes with stringy matter

Cited by in corpus (13)

• The Einstein-Vlasov System/Kinetic Theory
• The Einstein-Vlasov system/Kinetic theory
• Theorems on existence and global dynamics for the Einstein equations
• A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on T3
• Strong cosmic censorship for surface-symmetric cosmological spacetimes with collisionless matter
• Areal Foliation and AVTD Behavior in T^2 Symmetric Spacetimes with Positive Cosmological Constant
• Strong cosmic censorship for T^2-symmetric cosmological spacetimes with collisionless matter
• Static spherically symmetric Einstein-Vlasov bifurcations of the Schwarzschild spacetime
• Structure of solutions near the initial singularity for the surface-symmetric Einstein-Vlasov system
• On the area of the symmetry orbits of cosmological spacetimes with toroidal or hyperbolic symmetry
• On initial conditions and global existence for accelerating cosmologies from string theory
• Future $T^2$ symmetry Einstein-Vlasov-Scalar field system
• Local existence and continuation criteria for solutions of the Einstein-Vlasov-scalar field system with surface symmetry