Polish spaces of causal curves

Details

Written by Tomasz Miller

I will present a new approach to the topologization of the set of (possibly not all) causal curves on a stably causal spacetime. It relies on parametrizing the curves "in accordance" with a chosen time function. Thus obtained spaces turn out to possess certain nice topological and measure-theoretic properties - they are Polish.

In the second part of my talk, drawing from our earlier work on the causality between probability measures, I will discuss how the said Polish spaces of causal curves can be applied to the description of the causal time-evolution of spatially distributed physical quantities (like the charge or energy density) in globally hyperbolic spacetimes.

The talk will be mainly based on the preprint https://arxiv.org/abs/1609.09488