Causal completions as Lorentzian pre-length spaces

TL;DR

This paper explores the causal completion of globally hyperbolic spacetimes, framing it as a Lorentzian pre-length space, and extends this construction to specific generalized Robertson-Walker spacetimes.

Contribution

It introduces a novel approach to causal completions by structuring them as Lorentzian pre-length spaces, including for certain generalized Robertson-Walker spacetimes.

Findings

Causal completions can be structured as Lorentzian pre-length spaces.

The construction applies to a class of generalized Robertson-Walker spacetimes.

Provides a new geometric framework for understanding spacetime boundaries.

Abstract

In this work we revisit the notion of the (future) causal completion of a globally hyperbolic spacetime and endow it with the structure of a Lorentzian pre-length space. We further carry out this construction for a certain class of generalized Robertson-Walker spacetimes.