A class of anisotropic (Finsler-) space-time geometries

TL;DR

This paper classifies a broad class of Finsler space-time geometries with preferred directions, analyzing their symmetries and potential applications in testing space isotropy in relativistic theories.

Contribution

It introduces a classification of Finsler metrics with preferred directions based on their isometry groups, expanding understanding of anisotropic space-time geometries.

Findings

Finsler geometries have isometry groups isomorphic to subgroups of the Poincaré group plus dilatations.

The null-preferred Finsler space is the closest to isotropic Minkowski space within the class.

The geometries can be used to construct relativistic theories testing space isotropy.

Abstract

A particular Finsler-metric proposed in [1,2] and describing a geometry with a preferred null direction is characterized here as belonging to a subclass contained in a larger class of Finsler-metrics with one or more preferred directions (null, space- or timelike). The metrics are classified according to their group of isometries. These turn out to be isomorphic to subgroups of the Poincar\'e (Lorentz-) group complemented by the generator of a dilatation. The arising Finsler geometries may be used for the construction of relativistic theories testing the isotropy of space. It is shown that the Finsler space with the only preferred null direction is the anisotropic space closest to isotropic Minkowski-space of the full class discussed.