Analysis & Applied Math

Finsler spacetimes are a generalization of the concept of spacetime that take into account the directionality of the Lorentzian inner product in each tangent space. They provide a useful framework to study gravity beyond General Relativity, with applications in quantum gravity and extensions of the Standard Model.

In this talk, upon introducing and discussing the basic notions from Lorentzian and Lorentz-Finsler geometry, we turn our attention to the splitting problem for Finsler spacetimes of nonnegative (weighted) timelike Ricci curvature containing a timelike line. A splitting theorem in the Lorentz-Finsler setting was given by Lu-Minguzzi-Ohta under rather restrictive assumptions, which we are able to remove with the help of the elliptic p-d'Alembertian operator, which was recently used by Braun-Gigli-McCann-O.-Sämann to vastly simplify the classical Eschenburg-Galloway-Newman splitting theorems from spacetime geometry. This new version of the Lorentz-Finsler splitting theorem is much closer to the Riemann-Finsler splitting theorem due to Ohta, which generalizes the classical Cheeger-Gromoll result.

This talk is based on the joint work arxiv:2412.20783 together with Erasmo Caponio (Polytechn. Bari) and Shin-ichi Ohta (Osaka U.).