Geometry of weighted Lorentz-Finsler manifolds II: A splitting theorem

Abstract

We show an analogue of the Lorentzian splitting theorem for weighted Lorentz-Finsler manifolds: If a weighted Berwald spacetime of nonnegative weighted Ricci curvature satisfies certain completeness and metrizability conditions and includes a timelike straight line, then it necessarily admits a one-dimensional family of isometric translations generated by the gradient vector field of a Busemann function. Moreover, our formulation in terms of the $\epsilon$-range introduced in our previous work enables us to unify the previously known splitting theorems for weighted Lorentzian manifolds by Case and Woolgar-Wylie into a single framework.

28 pages, to appear in Internat. J. Math

References in corpus (2)

• Light cones in Finsler spacetime
• Limit curve theorems in Lorentzian geometry

Cited by in corpus (1)

• Concavity of spacetimes