Comparison theorems for Lorentzian length spaces with lower timelike curvature bounds

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 l...

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Bibliographic Details
Published in:General relativity and gravitation 2022-09, Vol.54 (9), Article 107
Main Authors: Barrera, Waldemar, de Oca, Luis Montes, Solis, Didier A.
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Cosmology
Classical and Quantum Gravitation
Convexity
Curvature
Differential Geometry
Gravity
Mathematical and Computational Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Research Article
Theorems
Theoretical
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Summary: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.
ISSN:0001-7701
1572-9532
DOI:10.1007/s10714-022-02989-2