Finsler spacetimes and gravity
  We consider the geometry of spacetime based on a non-metric, Finslerian, length measure, which, in terms of physics, represents a generalized clock. Our defnition of Finsler spacetimes ensure a well defined notion of causality, a precise description of observers and a geometric background for field theories. Moreover we present our Finsler geometric extension of the Einstein equations, which determine the geometry of Finsler spacetimes dynamically. 
Christian Pfeifer, Mattias N. R. Wohlfarth
gr-qc math-ph math.MP