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- Title
Comparison theorems for Lorentzian length spaces with lower timelike curvature bounds.
- Authors
Barrera, Waldemar; de Oca, Luis Montes; Solis, Didier A.
- Abstract
In this article we introduce a notion of normalized angle for Lorentzian pre-length spaces. This concept allows us to prove some equivalences to the definition of timelike curvature bounds from below for Lorentzian pre-length spaces. Specifically, we establish some comparison theorems known as the local Lorentzian version of the Toponogov theorem and the Alexandrov convexity property. Finally, as an application we obtain a first variation formula for non-negatively curved globally hyperbolic Lorentzian length spaces.
- Subjects
CURVATURE; TRIANGLES; DEFINITIONS
- Publication
General Relativity & Gravitation, 2022, Vol 54, Issue 9, p1
- ISSN
0001-7701
- Publication type
Article
- DOI
10.1007/s10714-022-02989-2