Related papers: Hausdorff closed limits and rigidity in Lorentzian…
In this work, we prove a synthetic splitting theorem for globally hyperbolic Lorentzian length spaces with global non-negative timelike curvature containing a complete timelike line. Just like in the case of smooth spacetimes, we construct…
We prove a transverse diameter theorem in the context of Lorentzian foliations, which can be interpreted as a Hawking--Penrose-type singularity theorem for timelike geodesics transverse to the foliation. In order to develop the necessary…
We study the question of local and global uniqueness of completions, based on null geodesics, of Lorentzian manifolds. We show local uniqueness of such boundary extensions. We give a necessary and sufficient condition for existence of…
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 smoothly isometric. A similar result holds for weighted…
We introduce conformal transformations in the synthetic setting of metric spaces and Lorentzian (pre-)length spaces. Our main focus lies on the Lorentzian case, where, motivated by the need to extend classical notions to spaces of low…
Certain closed-universe big-bang/big-crunch cosmological spacetimes may be obtained by analytic continuation from asymptotically AdS Euclidean wormholes, as emphasized by Maldacena and Maoz. We investigate how these Euclidean wormhole…
Timelike sectional curvature bounds play an important role in spacetime geometry, both for the understanding of classical smooth spacetimes and for the study of Lorentzian (pre-)length spaces introduced in \cite{kunzinger2018lorentzian}. In…
As one of the possible extensions of Einstein's General Theory of Relativity, it has been recently suggested that the presence of spacetime torsion could solve problems of the very early and the late-time universe undergoing accelerating…
We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds, where one has a lower bound on the Ricci tensor along timelike curves, and an upper bound on…
The Lorentzian metric structure used in any field theory allows one to implement the relativistic notion of causality and to define a notion of time dimension. This article investigates the possibility that at the microscopic level the…
Some well-known Lorentzian concepts are transferred into the more general setting of cone structures, which provide both the causality of the spacetime and the notion of cone geodesics without making use of any metric. Lightlike…
We consider four-dimensional general relativity with vanishing cosmological constant defined on a manifold with a boundary. In Lorentzian signature, the timelike boundary is of the form $\boldsymbol{\sigma} \times \mathbb{R}$, with…
We prove a globally hyperbolic spacetime with locally Lipschitz continuous metric and timelike distributional Ricci curvature bounded from below obeys the timelike measure contraction property. The remarkable class of examples of spacetimes…
We prove new estimates for the volume of a Lorentzian manifold and show especially that cosmological spacetimes with crushing singularities have finite volume.
In this paper we study the rigidity problem for sub-static systems with possibly non-empty boundary. First, we get local and global splitting theorems by assuming the existence of suitable compact minimal hypersurfaces, complementing recent…
Classical Kleinian groups are discrete subgroups of isometries of H n. The well-known theory of Kleinian groups starts with the definition of their associated limit set in the boundary of H n , and includes the geometric properties of the…
Following Geroch, Traschen, Mars and Senovilla, we consider Lorentzian manifolds with distributional curvature tensor. Such manifolds represent spacetimes of general relativity that possibly contain gravitational waves, shock waves, and…
In this short note we argue that, even if, as sometimes remarked, a Lorentzian manifold does not model correctly the structure of the spatio-temporal continuum as it is, yet a Lorentzian manifold should describe its macroscopic structure as…
The Raychaudhuri equation and its consequences for chronality are studied in the context of Finsler spacetimes. It is proved that the notable singularity theorems of Lorentzian geometry extend to the Finslerian domain. Indeed, so do the…
This thesis explores the thermodynamics of the cosmological horizon, aiming to make progress towards a better understanding of the microscopic nature of its entropy. We utilise the constrained nature of low-dimensional gravity to do so and…