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

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

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