  Inspired by the results in a recent paper by G. Galloway and C. Vega (see
arXiv:1712.00785), we investigate a number of geometric consequences of the
existence of a timelike conformal Killing vector field on a globally hyperbolic
spacetime with compact Cauchy hypersurfaces, especially in connection with the
so-called Bartnik's splitting conjecture. In particular we give a complementary
result to the main theorem in Galloway and Vega's paper.
