Existence and non-existence results for global constant mean curvature foliations

Details Existence and non-existence results for global constant mean curvature foliations Existence and non-existence results for global constant mean curvature foliations

1996-08-19

arxiv.org/abs/gr-qc/9608045v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages. Contribution to proceedings of 2nd World Congress of Nonlinear Analysts

Scientific paper

The main result of this paper is a proof that there are examples of spatially compact solutions of the Einstein-dust equations which only exist for an arbitrarily small amount of CMC time. While this fact is plausible, it is not trivial to prove. It is necessary to obtain a lower bound for the lapse function of a CMC foliation in a suitable class of inhomogeneous spacetimes. This bound, which shows that in these spacetimes the lapse cannot collapse in finite CMC time, may be of independent interest. This fact is contrasted with the positive results previously obtained for other matter models, e.g. collisionless matter or wave maps.

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