6 papers
The Penrose singularity theorem, MOTS stability, and horizon topology in weighted spacetimes
Eric Ling, Argam Ohanyan, Eric Woolgar
We consider versions of the Penrose singularity theorem and the Hawking horizon topology theorem in weighted spacetimes that contain weighted versions of trapped surfaces, for arbi…
Timelike conjugate points in Lorentzian length spaces
James D. E. Grant, Michael Kunzinger, Argam Ohanyan +2
We study notions of conjugate points along timelike geodesics in the synthetic setting of Lorentzian (pre-)length spaces, inspired by earlier work for metric spaces by Shankar--Sor…
Topological cones and positively polarizable hyperbolic norms
Ethan Kharitonov, Argam Ohanyan
In the first part of this article, we study linear cones over totally ordered fields. We show that for each such cone there uniquely exists a universal vector space (called its spa…
Generalizing the Penrose cut-and-paste method: Null shells with pressure and energy flux
Miguel Manzano, Argam Ohanyan, Roland Steinbauer
The cut-and-paste method is a procedure for constructing null thin shells by matching two regions of the same spacetime across a null hypersurface. Originally proposed by Penrose,…
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…
Distributional sectional curvature bounds for Riemannian metrics of low regularity
Darius Erös, Michael Kunzinger, Argam Ohanyan +1
Sectional curvature bounds are of central importance in the study of Riemannian manifolds, both in smooth differential geometry and in the generalized synthetic setting of Alexandr…