Comparison theorems for Lorentzian length spaces with lower timelike curvature bounds

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.

References in corpus (5)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• The causal set approach to quantum gravity
• Globally hyperbolic spacetimes can be defined as "causal" instead of "strongly causal"
• On the causal hierarchy of Lorentzian length spaces

Cited by in corpus (4)

• The splitting theorem for globally hyperbolic Lorentzian length spaces with non-negative timelike curvature
• Hyperbolic angles in Lorentzian length spaces and timelike curvature bounds
• Causal completions as Lorentzian pre-length spaces
• Gluing of Lorentzian length spaces and the causal ladder