Gluing of Lorentzian length spaces and the causal ladder

TL;DR

This paper studies how gluing Lorentzian length spaces affects their causal properties, providing conditions for preserving the structure and exploring challenges in transferring certain causal features.

Contribution

It offers new criteria for gluing Lorentzian length spaces that maintain their causal ladder properties and discusses difficulties in transferring some causal characteristics.

Findings

Provided conditions for successful gluing of Lorentzian length spaces.

Identified properties preserved under gluing.

Highlighted causal properties that are difficult to transfer.

Abstract

We investigate the compatibility of Lorentzian amalgamation with various properties of Lorentzian pre-length spaces. In particular, we give conditions under which gluing of Lorentzian length spaces yields again a Lorentzian length space and we give criteria which preserve many steps of the causal ladder. We conclude with some thoughts on the causal properties which seem not so easily transferable.