Finsler geometric extension of Einstein gravity

Abstract

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. Moreover, we discuss the implementation of Finsler spacetime symmetries. We use our results to analyze a particular spacetime model that leads to Finsler geometric refinements of the linearized Schwarzschild solution.

39 pages, 4 figures, journal references added

References in corpus (2)

• Modified Newton's gravity in Finsler Space as a possible alternative to dark matter hypothesis
• Modified Friedmann model in Randers-Finsler space of approximate Berwald type as a possible alternative to dark energy hypothesis

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