Geometry of weighted Lorentz-Finsler manifolds I: Singularity theorems

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.

37 pages; some modifications to clarify motivation and improve presentation; to appear in J. Lond. Math. Soc

References in corpus (5)

• Causality theory for closed cone structures with applications
• Light cones in Finsler spacetime
• An optimal transport formulation of the Einstein equations of general relativity
• Chronological spacetimes without lightlike lines are stably causal
• Inextendibility of spacetimes and Lorentzian length spaces

Cited by in corpus (6)

• A review of Lorentzian synthetic theory of timelike Ricci curvature bounds
• A Lorentzian analog for Hausdorff dimension and measure
• Spinors and mass on weighted manifolds
• Geometry of weighted Lorentz-Finsler manifolds II: A splitting theorem
• A variational setting for an indefinite Lagrangian with an affine Noether charge
• Concavity of spacetimes