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

Abstract

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.

33 pages, no figures

References in corpus (3)

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

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