Geometry of weighted Lorentz–Finsler manifolds I: singularity theorems
Yufeng Lu, Ettore Minguzzi, Shin‐ichi Ohta
Abstract
We develop the theory of weighted Ricci curvature in a weighted Lorentz–Finsler framework and extend the classical singularity theorems of general relativity. In order to reach this result, we generalize the Jacobi, Riccati and Raychaudhuri equations to weighted Finsler spacetimes and study their implications for the existence of conjugate points along causal geodesics. We also show a weighted Lorentz–Finsler version of the Bonnet–Myers theorem based on a generalized Bishop inequality.
Topics & Concepts
MathematicsSingularityConjugate pointsOrder (exchange)Pure mathematicsCurvatureSingularity theoryRicci curvatureGravitational singularityDifferential geometryMathematical analysisSectional curvatureIsolated singularityEssential singularityRiccati equationRiemannian geometryMean curvatureRiemann curvature tensorComparison theoremGeometryAdvanced Differential Geometry ResearchGeometric Analysis and Curvature FlowsNoncommutative and Quantum Gravity Theories