Observable effects in a class of spherically symmetric static Finsler spacetimes

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 ₀ (r), ₁ (r) and ₂ (r) which have the following interpretations: ₀ perturbs the time function, ₁ perturbs the radial length measurement and 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.