1998/10/18 by Mihaela Time, Time, Mihaela
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/9810059
6 pages, LaTeX
arxiv created 1998/10/18 · arxiv updated 2009/11/30
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 + T0 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 omega0 = 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.