Gluing constructions for Lorentzian length spaces

Abstract

We introduce an analogue to the amalgamation of metric spaces into the setting of Lorentzian pre-length spaces. This provides a very general process of constructing new spaces out of old ones. The main application in this work is an analogue of the gluing theorem of Reshetnyak for CAT($k$) spaces, which roughly states that gluing is compatible with upper curvature bounds. We formulate the theorem in terms of (strongly causal) spacetimes viewed as Lorentzian length spaces.

arXiv comment39 pages, 14 figures

References in corpus (7)

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• Null distance and convergence of Lorentzian length spaces
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Cited by in corpus (5)

• The splitting theorem for globally hyperbolic Lorentzian length spaces with non-negative timelike curvature
• Hyperbolic angles in Lorentzian length spaces and timelike curvature bounds
• Causal completions as Lorentzian pre-length spaces
• A Toponogov globalisation result for Lorentzian length spaces
• A lower semicontinuous time separation function for $C^0$ spacetimes