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arXiv · 2302.11819

On the space of compact diamonds of Lorentzian length spaces

Waldemar Barrera·Luis Montes de Oca·Didier A. Solis
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Abstract

In this work we introduce the taxicab and uniform products for Lorentzian pre-length spaces. We further use these concepts to endow the space $D(R\times_T X)$ of causal diamonds with a Lorentzian length space structure, closely relating its causal properties with its geometry as a metric space furnished with its associated Hausdorff distance. Among the general results, we show that this space is geodesic and globally hyperbolic for complete $X$.

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Waldemar Barrera, Luis Montes de Oca, Didier A. Solis. 2023-02-23. On the space of compact diamonds of Lorentzian length spaces. https://arxiv.org/abs/2302.11819

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