A volume element on time orientable Finslerian spacetimes

TL;DR

This paper introduces a new volume element for Lorentzian Finsler spacetimes with a time orientation, extending Holmes-Thompson volume concepts to indefinite metrics for potential field-theoretical applications.

Contribution

It proposes a Lorentzian Finsler volume element based on Holmes-Thompson ideas, independent of the chosen time orientation, suitable for field theory on Finsler backgrounds.

Findings

Defines a Lorentzian Finsler volume element

Independent of time orientation choice

Applicable to field-theoretical models

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.