We introduce an analogue of the theory of length spaces into the setting of Lorentzian
geometry and causality theory. The rôle of the metric is taken over by the time separation …

The goal of the present work is three-fold. The first goal is to set foundational results on
optimal transport in Lorentzian (pre-) length spaces, including cyclical monotonicity, stability …

For a Lorentzian space measured by m in the sense of Kunzinger, Sämann, Cavalletti, and
Mondino, we introduce and study synthetic notions of timelike lower Ricci curvature bounds …

In general relativity, time functions are crucial objects whose existence and properties are
intimately tied to the causal structure of a spacetime and also to the initial value formulation …

The null distance of Sormani and Vega encodes the manifold topology as well as the
causality structure of a (smooth) spacetime. We extend this concept to Lorentzian length …

We define a one-parameter family of canonical volume measures on Lorentzian (pre-)
length spaces. In the Lorentzian setting, this allows us to define a geometric dimension …

Within the synthetic‐geometric framework of Lorentzian (pre‐) length spaces developed in
Kunzinger and Sämann (Ann. Glob. Anal. Geom. 54 (2018), no. 3, 399–447) we introduce a …

We study generalizations of Lorentzian warped products with one-dimensional base of the
form $ I\times_f X $, where $ I $ is an interval, $ X $ is a length space and $ f $ is a positive …

We give a simpler approach to Kunzinger and Sämann's theory of Lorentzian length spaces
in the globally hyperbolic case; these provide a nonsmooth framework for general relativity …

We introduce a variational first-order Sobolev calculus on metric measure spacetimes. The
key object is the maximal weak subslope of an arbitrary causal function, which plays the role …