2016/09/30 by Tomasz Miller
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Causal sets #Causal structure #Causality (physics) #Computer science #Cosmology and Gravitation Theories #Epistemology #Function (biology) #Interpretation (philosophy) #Mathematical analysis #Mathematics #Metrization theorem #Physics #Property (philosophy) #Pure mathematics #Quantum gravity #Separable space #Spacetime #math-ph #math.MP #msc:28E99 #msc:53C50 #msc:53C80 #msc:60B05
paper · pdf · doi:10.1016/j.geomphys.2017.02.006
published as J. Geom. Phys. 2017, 116, 295-315 · 32 pages
openalex publication_date 2017/02/17 · arxiv created 2018/03/08 · arxiv updated 2018/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose and study a new approach to the topologization of spaces of (possibly not all) future-directed causal curves in a stably causal spacetime. It relies on parametrizing the curves "in accordance" with a chosen time function. Thus obtained topological spaces of causal curves are separable and completely metrizable, i.e. Polish. The latter property renders them particularly useful in the optimal transport theory. To illustrate this fact, we explore the notion of a causal time-evolution of measures in globally hyperbolic spacetimes and discuss its physical interpretation.