Space-time distributions.pdfVIP

Space-time distributions Mihaela D. Iftime 8 9 9 31 Aug 98 1 t c O Abstract 8 The space-time foliation Σ compatible with the gravitational field 1 g on a 4-manifold M determines a fibration π of M , π : M −→ N is a surjective submersion over the 1-dimensional leaves space N . M is then 1 written as a disjoint union of the leaves of Σ, which are 3-dimensional v spacelike surfaces on M . 9 0 5 The decomposition, T M = Σ ⊕ T M , also implies that we can 0 define a lift of the curves on N to curves (non-spacelike) on M . 0 The stable causality condition M [2] coincides with Σ being a causal 1 space-time distribution, generated by an exact timelike 1-form ω0 = dt 8 where t is some real function on M . In this case M is written as a 9 / disjoint union of a family of spacelike 3-surfaces of constant t, which c cover D+ (S) of a initial 3-surface S of M . q - r g AMS Classification numbers: : Primary: 83C99 v i Secondary: 53B30 53C50 53C12 57R30 X r Keywords: space-time distribution, 4-manifold a 1 1 Introduction Note: We will denote by small Latin indices a, b, . . . numbers ranging from 0 to 3 and the small Greek indices α, β, . . . numbers