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A Lorentzian splitting theorem for continuously differentiable metrics and weights
Mathias Braun, Nicola Gigli, Robert J. McCann +2
We prove a splitting theorem for globally hyperbolic, weighted spacetimes with metrics and weights of regularity by combining elliptic techniques for the negative homogeneity…
Spacetime reconstruction by order and number
Mathias Braun
We show that the random adjacency matrices induced by the chronological relations and i.i.d. samples of two spacetimes coincide in law if and only if the spacetimes in question are…
Gromov's reconstruction theorem and measured Gromov-Hausdorff convergence in Lorentzian geometry
Mathias Braun, Clemens Sämann
We establish Gromov's celebrated reconstruction theorem in Lorentzian geometry. Alongside this result, we introduce and study a natural concept of isomorphy of normalized bounded L…
New perspectives on the d'Alembertian from general relativity. An invitation
Mathias Braun
This survey has multiple objectives. First, we motivate and review a new distributional notion of the d'Alembertian from mathematical relativity, more precisely, a nonlinear -ve…