Geometry of weighted Lorentz–Finsler manifolds I: singularity theorems

We develop the theory of weighted Ricci curvature in a Lorentz-Finsler framework and extend classical singularity theorems general relativity. In order to reach this result, we generalize Jacobi, Riccati Raychaudhuri equations Finsler spacetimes study their implications for existence conjugate points along causal geodesics. also show version Bonnet-Myers theorem based on generalized Bishop inequality.