Mathematical foundations for field theories on Finsler spacetimes

This paper introduces a general mathematical framework for action-based field theories on Finsler spacetimes. As most often fields on Finsler spacetime (e.g., the Finsler fundamental function or the resulting metric tensor) have a homogeneous dependence on the tangent directions of spacetime, we construct the appropriate configuration bundles whose sections are such homogeneous fields; on these configuration bundles, the tools of coordinate free calculus of variations can be consistently applied to obtain field equations. Moreover, we prove that the general covariance of natural Finsler field Lagrangians leads to an averaged energy-momentum conservation law that, in the particular case of Lorentzian spacetimes, is equivalent to the usual pointwise energy-momentum covariant conservation law. Published under an exclusive license by AIP Publishing.

Automated summary

This paper introduces a mathematical framework for action-based field theories on Finsler spacetimes and discusses the construction of appropriate configuration bundles and the use of coordinate free calculus of variations. It also proves the general covariance of natural Finsler field Lagrangians and their equivalence to the usual pointwise energy-momentum covariant conservation law in Lorentzian spacetimes.