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math.DG2026
Ideal points, directed completion and the case of the maximally extended Schwarzschild spacetime
Nicola Gigli, Argam Ohanyan, Marco Picerni +2
We study the directed completion of Lorentzian pre-length spaces, and we show that, under some natural assumptions which cover the case of smooth globally hyperbolic spacetimes, it…
math.DG2026
Submetries in non-positive signature and applications
Matteo Zanardini
We consider a generalization of the notion of submetry tailored to the setting of spacetimes. We show that, under suitable completeness assumptions, Lorentzian submetries between s…
math.DG2026
Lorentz meets Ptolemy
Felix Rott, Zhe-Feng Xu, Matteo Zanardini
We consider a Lorentzian analogue of the Ptolemy inequality and we prove that in the setting of globally hyperbolic spacetimes it is equivalent to a global timelike sectional curva…