The causal structure of the c-completion of warped spacetimes

In this work we study the structure of the future causal completion $\hat{M}$ of a globally hyperbolic GRW spacetime $\mathbb{R}\times_\alpha M$ using the novel notion of Lorentzian pre-length spaces. As our main result, we prove that the causal completion of a GRW spacetime is a globally hyperbolic pre-length space provided the chronological topology is Hausdorff.