The m-th root Finsler geometry of the Bogoslovsky-Goenner metric

TL;DR

This paper explores the m-th root Finsler geometries of the Bogoslovsky-Goenner metrics in 3D and 4D, analyzing their Cartan torsion, curvature tensors, and Einstein-like equations to understand their anisotropic properties in special relativity.

Contribution

It introduces the m-th root Finsler geometries for these metrics and examines their geometric properties, providing new insights into their structure in the context of anisotropic models.

Findings

Derived the Finsler geometries for 3D and 4D Bogoslovsky-Goenner metrics.

Analyzed Cartan torsion and curvature tensors of these geometries.

Formulated vertical Einstein-like equations for the models.

Abstract

In this paper we present the m-th root Finsler geometries of the three and four dimensional Bogoslovsky-Goenner metrics (good Finslerian anisotropic models in Special Relativity), in the sense of their Cartan torsion and curvature distinguished tensors or vertical Einstein-like equations.