A Model for the Pioneer Anomaly
  In a previous work we showed that massive test particles exhibit a non-geodesic acceleration in a modified theory of gravity obtained by a non-commutative deformation of General Relativity (so-called Matrix Gravity). We propose that this non-geodesic acceleration might be the origin of the anomalous acceleration experienced by the Pioneer 10 and Pioneer 11 spacecrafts. 
Ivan G. Avramidi and Guglielmo Fucci