Observable effects in a class of spherically symmetric static Finsler spacetimes

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 $ϕ_0(r)$, $ϕ_1(r)$ and $ϕ_2(r)$ which have the following interpretations: $ϕ_0$ perturbs the time function, $ϕ_1$ perturbs the radial length measurement and $ϕ_2$ 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.