Geodesics and the magnitude-redshift relation on cosmologically symmetric Finsler spacetimes

TL;DR

This paper investigates geodesic motion and the magnitude-redshift relation in cosmologically symmetric Finsler spacetimes, deriving equations and constants of motion to compare theoretical models with supernova observations.

Contribution

It derives the general geodesic equations and constants of motion for Finsler spacetimes with cosmological symmetry, and applies these to the magnitude-redshift relation for observational tests.

Findings

Derived geodesic equations for Finsler spacetimes.

Established constants of motion for these geodesics.

Applied results to specific Finsler models like Bogoslovsky and Randers.

Abstract

We discuss the geodesic motion of both massive test particles, following timelike geodesics, and light, following null geodesics, on Finsler spacetimes with cosmological symmetry. Using adapted coordinates on the tangent bundle of the spacetime manifold, we derive the general form of the geodesic equation. Further, we derive a complete set of constants of motion. As an application of these findings, we derive the magnitude-redshift relation for light propagating on a cosmologically symmetric Finsler background, both for a general Finsler spacetime and for particular examples, such as spacetimes equipped with Bogoslovsky and Randers length measures. Our results allow a confrontation of these geometries with observations of the magnitude and redshift of supernovae.