Splitting theorems appear in many areas of geometry and roughly state that a (complete) space of nonnegative curvature containing a global line splits isometrically into a product. In Lorentzian geometry, the splitting theorem was established in the 1990-ies by distinct contributions from a number of researchers.

In this talk, we present current work on the splitting theorem for globally hyperbolic Lorentzian length spaces whose timelike curvature is globally bounded below by 0. Taking a similar approach as in the positive definite synthetic case, we investigate the notion of parallelity for timelike lines. It turns out that timelike asymptotes to a given timelike line are all parallel to each other, and there is a well-defined notion of normal distance between them. This allows us to equip a cross-section of these lines with a metric structure which represents the metric factor in the splitting.

This is joint work with Tobias Beran, Felix Rott and Didier A. Solis.