Finsler geometric extension of Einstein gravity

Understand

We construct gravitational dynamics for Finsler spacetimes in terms of an action integral on the unit tangent bundle.

• These spacetimes are generalizations of Lorentzian metric manifolds which satisfy necessary causality properties.
• A coupling procedure for matter fields to Finsler gravity completes our new theory that consistently becomes equivalent to Einstein gravity in the limit of metric geometry.
• We provide a precise geometric definition of observers and their measurements, and show that the transformations by means of which different observers communicate form a groupoid that generalizes the usual Lorentz group.