Some Remarks on Conformal Symmetries and Bartnik’s Splitting Conjecture

Inspired by the results in a recent paper by Galloway and Vega (Lett Math Phys 108(10):2285–2292, 2018), we investigate a number of geometric consequences of the existence of a timelike conformal Killing vector field in a globally hyperbolic space-time 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 [11].