On the area of the symmetry orbits of cosmological spacetimes with toroidal or hyperbolic symmetry

Details On the area of the symmetry orbits of cosmological spacetimes with toroidal or hyperbolic symmetry On the area of the symmetry orbits of cosmological spacetimes with toroidal or hyperbolic symmetry

2009-04-06

arxiv.org/abs/0904.0806v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

70 pages, 2 tables

Scientific paper

We prove several global existence theorems for spacetimes with toroidal or hyperbolic symmetry with respect to a geometrically defined time. More specifically, we prove that generically, the maximal Cauchy development of $T^2$-symmetric initial data with positive cosmological constant $\Lambda >0$, in the vacuum or with Vlasov matter, may be covered by a global areal foliation with the area of the symmetry orbits tending to zero in the contracting direction. We then prove the same result for surface symmetric spacetimes in the hyperbolic case with Vlasov matter and $\Lambda \ge 0$. In all cases, there is no restriction on the size of initial data.

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