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

TL;DR

This paper explores how Finsler geometry, specifically Randers space, can explain the Pioneer anomaly by deriving an additional acceleration term in geodesic equations.

Contribution

It introduces a Finsler geometric framework that models the Pioneer anomaly as a natural consequence of geodesic motion in Randers space.

Findings

Finsler structure explains the Pioneer anomalous acceleration

The additional term acts like an electric force in geodesic equations

Provides a geometric basis for the Pioneer anomaly

Abstract

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.