Reference: Topology in General Relativity (R. P. Geroch, J. Math. Phys. 8(4) April 1967)
Geroch's "Splitting" Theorem (Theorem 2) applies to spacetimes with compact geometries with boundary. Minkowski space is not a compact geometry.
Can Geroch's result nonetheless be extended to Minkowski spacetime by adding conformal infinity as boundaries, on the bounding spacelike 3-manifolds etc.?
A pedagogical answer either way would be much appreciated (as would any info on how then to handle the isometries of such a Minkowski spacetime with conformal infinity boundary)
Statement of the theorem (quote from reference)
Let $M$ be a compact geometry whose boundary is the disjoint union of two compact space-like 3-manifolds, $S$ and $S'$. Suppose $M$ is isochronous, and has no closed timelike curve. Then $S$ and $S'$ are diffeomorphic [Wikipedia says, incorrectly, merely homeomorphic], and further $M$ is topologically $S \times[0,1]$.
The interest is in the construction and use of the non-vanishing timelike vector fields used in the proof, which relates to Theorem 1 ibid. (Rohklin) and the equivalence of such vector fields, given that "the problem of placing a Lorentz signature metric is equivalent" (Steenrod cited) to that of placing a continuous, nowhere vanishing vector field on $M$ (and nowhere tangent to the boundaries).