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Space-time distributions

Mihaela Time
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Abstract

The space-time foliation Sigma compatible with the gravitational field g on a 4-manifold M determines a fibration pi of M, pi : M -> N is a surjective submersion over the 1-dimensional leaves space N. M is then written as a disjoint union of the leaves of Sigma, which are 3-dimensional spacelike surfaces on M. The decomposition, TM=Sigma + T^0 M, also implies that we can define a lift of the curves on N to curves (non-spacelike) on M. The stable causality condition M coincides with Sigma being a causal space-time distribution, generated by an exact timelike 1-form omega^0 = dt where t is some real function on M. In this case M is written as a disjoint union of a family of spacelike 3-surfaces of constant t, which cover D^+(S) of a initial 3-surface S of M.

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Mihaela Time. 1998-10-18. Space-time distributions. https://arxiv.org/abs/gr-qc/9810059

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