A divergence theorem for pseudo-Finsler spaces

TL;DR

This paper develops a divergence theorem for pseudo-Finsler spaces with zero mean Cartan torsion, aiding the understanding of energy-momentum conservation in Finsler gravity theories.

Contribution

It provides a fully Finslerian divergence theorem for specific pseudo-Finsler spaces, addressing a key issue in Finsler gravity.

Findings

Derived a divergence theorem for pseudo-Finsler spaces with vanishing mean Cartan torsion.

Clarified the role of the divergence theorem in energy-momentum conservation in Finsler gravity.

Enhanced mathematical tools for studying Finslerian geometric structures.

Abstract

We study the divergence theorem on pseudo-Finsler spaces and obtain a completely Finslerian version for spaces having a vanishing mean Cartan torsion. This result helps to clarify the problem of energy-momentum conservation in Finsler gravity theories.