Gluing of Lorentzian length spaces and the causal ladder

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.

27 pages, 4 figures

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Cited by in corpus (3)

• The splitting theorem for globally hyperbolic Lorentzian length spaces with non-negative timelike curvature
• A Toponogov globalisation result for Lorentzian length spaces
• A lower semicontinuous time separation function for $C^0$ spacetimes