Hyperbolic angles in Lorentzian length spaces and timelike curvature bounds

Abstract

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 hyperbolic angle, an angle between timelike curves and related concepts like timelike tangent cone and exponential map. This provides valuable technical tools for the further development of the theory and paves the way for the main result of the article, which is the characterization of timelike curvature bounds (defined via triangle comparison) with an angle monotonicity condition. Further, we improve on a geodesic non-branching result for spaces with timelike curvature bounded below.

72 pages, 15 figures; v4: fixed missing case in Thm. 4.5, results unchanged

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Cited by in corpus (5)

• Causal completions as Lorentzian pre-length spaces
• Gluing of Lorentzian length spaces and the causal ladder
• A Toponogov globalisation result for Lorentzian length spaces
• A lower semicontinuous time separation function for $C^0$ spacetimes
• Concavity of spacetimes