28 citations · 172 across the 17 of their papers we have counts for
19 papers
Doubling for chronological diamonds in Lorentzian geometry
Mauricio Che, Sebastian Gieger, Clemens Sämann
We define doubling conditions for measured Lorentzian length spaces in terms of chronological diamonds, and prove that such conditions are implied by suitable timelike curvature bo…
Stability of Synthetic Timelike Ricci Bounds under -Limits and Applications to Impulsive Gravitational Waves
Andrea Mondino, Vanessa Ryborz, Clemens Sämann
We investigate the stability of timelike Ricci curvature lower bounds under low-regularity limits of Lorentzian metrics. Specifically, we prove that the synthetic curvature-dimensi…
Curvature bounds, regularity and inextendibility of spacetimes
Tobias Beran, John Harvey, Clemens Sämann
We provide a completely new relation between curvature bounds and definiteness of the causal character of maximizers by exploiting the robust notion of synthetic curvature. This en…
An elliptic proof of the splitting theorems from Lorentzian geometry
Mathias Braun, Nicola Gigli, Robert J. McCann +2
We provide a new proof of the splitting theorems from Lorentzian geometry, in which simplicity is gained by sacrificing linearity of the d'Alembertian to recover ellipticity. We ex…
Cut-and-paste for impulsive gravitational waves with : The mathematical analysis
Clemens Sämann, Benedict Schinnerl, Roland Steinbauer +1
Impulsive gravitational waves are theoretical models of short but violent bursts of gravitational radiation. They are commonly described by two distinct spacetime metrics, one of l…
Hyperbolic angles in Lorentzian length spaces and timelike curvature bounds
Tobias Beran, Clemens Sämann
Within the synthetic-geometric framework of Lorentzian (pre-)length spaces developed in Kunzinger and Sämann (Ann. Glob. Anal. Geom. 54(3):399--447, 2018) we introduce a notion of…
A Lorentzian analog for Hausdorff dimension and measure
Robert J. McCann, Clemens Sämann
We define a one-parameter family of canonical volume measures on Lorentzian (pre-)length spaces. In the Lorentzian setting, this allows us to define a geometric dimension - akin to…
Lorentz meets Lipschitz
Christian Lange, Alexander Lytchak, Clemens Sämann
We show that maximal causal curves for a Lipschitz continuous Lorentzian metric admit a -parametrization and that they solve the geodesic equation in the sense o…
Generalized cones as Lorentzian length spaces: Causality, curvature, and singularity theorems
Stephanie B. Alexander, Melanie Graf, Michael Kunzinger +1
We study generalizations of Lorentzian warped products with one-dimensional base of the form , where is an interval, is a length space and is a positive co…
The future is not always open
James D. E. Grant, Michael Kunzinger, Clemens Sämann +1
We demonstrate the breakdown of several fundamentals of Lorentzian causality theory in low regularity. Most notably, chronological futures (defined naturally using locally Lipschit…
Lorentzian length spaces
Michael Kunzinger, Clemens Sämann
We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The rôle of the metric is taken over by the time separation fu…
On geodesics in low regularity
Clemens Sämann, Roland Steinbauer
We consider geodesics in both Riemannian and Lorentzian manifolds with metrics of low regularity. We discuss existence of extremal curves for continuous metrics and present several…
Penrose junction conditions extended: impulsive waves with gyratons
Jiri Podolsky, Robert Svarc, Roland Steinbauer +1
We generalize the classical junction conditions for constructing impulsive gravitational waves by the Penrose "cut and paste" method. Specifically, we study nonexpanding impulses w…
Geodesics in nonexpanding impulsive gravitational waves with , II
Clemens Sämann, Roland Steinbauer
We investigate all geodesics in the entire class of nonexpanding impulsive gravitational waves propagating in an (anti-)de Sitter universe using the distributional metric. We exten…
Completeness of general pp-wave spacetimes and their impulsive limit
Clemens Sämann, Roland Steinbauer, Robert Švarc
We investigate geodesic completeness in the full family of pp-wave or Brinkmann spacetimes in their extended as well as in their impulsive form. This class of geometries contains t…
The global uniqueness and -regularity of geodesics in expanding impulsive gravitational waves
Jiri Podolsky, Clemens Sämann, Roland Steinbauer +1
We study geodesics in the complete family of expanding impulsive gravitational waves propagating in spaces of constant curvature, that is Minkowski, de Sitter and anti-de Sitter un…
Geodesics in nonexpanding impulsive gravitational waves with , Part I
Clemens Sämann, Roland Steinbauer, Alexander Lecke +1
We investigate the geodesics in the entire class of nonexpanding impulsive gravitational waves propagating in an (anti-)de Sitter universe using the distributional form of the metr…
Global algebras of nonlinear generalized functions with applications in general relativity
Eduard A. Nigsch, Clemens Sämann
We give an overview of the development of algebras of generalized functions in the sense of Colombeau and recent advances concerning diffeomorphism invariant global algebras of gen…
Geodesic completeness of generalized space-times
Clemens Sämann, Roland Steinbauer
We define the notion of geodesic completeness for semi-Riemannian metrics of low regularity in the framework of the geometric theory of generalized functions. We then show complete…