A possible scenario of the Pioneer anomaly in the framework of Finsler geometry

The weak field approximation of geodesics in Randers–Finsler space is investigated. We show that a Finsler structure of Randers space corresponds to the constant and sunward anomalous acceleration demonstrated by the Pioneer 10 and 11 data. The additional term in the geodesic equation acts as “electric force”, which provides the anomalous acceleration.