# Geometry of weighted Lorentz-Finsler manifolds I: Singularity theorems

## TL;DR

This paper extends classical singularity theorems of general relativity to weighted Lorentz-Finsler manifolds by developing new curvature and geodesic equations, broadening the mathematical framework for spacetime singularities.

## Contribution

It introduces a weighted Ricci curvature theory in Lorentz-Finsler geometry and generalizes key equations, enabling new singularity theorems and geometric results.

## Key findings

- Generalized Jacobi, Riccati, and Raychaudhuri equations for weighted Finsler spacetimes
- Proved a weighted Lorentz-Finsler version of the Bonnet-Myers theorem
- Established conditions for conjugate points along causal geodesics

## 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.