Global Prescribed Mean Curvature foliations in cosmological spacetimes with matter, Part I

Details Global Prescribed Mean Curvature foliations in cosmological spacetimes with matter, Part I Global Prescribed Mean Curvature foliations in cosmological spacetimes with matter, Part I

2001-10-18

arxiv.org/abs/gr-qc/0110081v1

J.Math.Phys. 43 (2002) 2439-2465

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pages, no figures

Scientific paper

This work investigates some global questions about cosmological spacetimes with two dimensional spherical, plane and hyperbolic symmetry containing matter. The result is, that these spacetimes admit a global foliation by prescribed mean curvature surfaces, which extends at least towards a crushing singularity. The time function of the foliation is geometrically defined and unique up to the choice of an initial Cauchy surface. This work generalizes a similar analysis on constant mean curvature foliations and avoids the topological obstructions arising from the existence problem.

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