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

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

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27 pages, version 2 minor changes and corrections

Scientific paper

10.1088/0264-9381/21/4/023

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.

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