A volume element on time orientable Finslerian spacetimes

Abstract

The paper proposes a notion of volume element for Finsler spaces with metrics of Lorentzian signature, equipped with a time orientation. This notion is based on a slight modification of the idea of Holmes-Thompson volume element working for positive definite Finsler metrics and can be used in field-theoretical applications on a Finslerian background. Though the approach assumes the existence of a time orientation, the volume element does not depend on its choice.

This paper has been withdrawn by the author due to an error in the statement according to which the volume element does not depend on the choice of the time orientation