Observable effects in a class of spherically symmetric static Finsler spacetimes

TL;DR

This paper explores how small Finslerian deviations from Schwarzschild spacetime could produce observable effects, analyzing geodesics and setting bounds based on Solar system observations.

Contribution

It introduces a class of spherically symmetric static Finsler spacetimes with three perturbation functions and derives their geodesic equations, linking Finsler features to observable phenomena.

Findings

Perturbation functions affect geodesic motion.

Solar system observations constrain Finsler deviations.

Spatial anisotropy is a genuine Finsler feature.

Abstract

After some introductory discussion of the definition of Finsler spacetimes and their symmetries, we consider a class of spherically symmetric and static Finsler spacetimes which are small perturbations of the Schwarzschild spacetime. The deviations from the Schwarzschild spacetime are encoded in three perturbation functions $\phi_0(r)$, $\phi_1(r)$ and $\phi_2(r)$ which have the following interpretations: $\phi_0$ perturbs the time function, $\phi_1$ perturbs the radial length measurement and $\phi_2$ introduces a spatial anisotropy which is a genuine Finsler feature. We work out the equations of motion for freely falling particles and for light rays, i.e. the timelike and lightlike geodesics, in this class of spacetimes, and we discuss the bounds placed on the perturbation functions by observations in the Solar system.