Finsler geometric extension of Einstein gravity

Details Finsler geometric extension of Einstein gravity Finsler geometric extension of Einstein gravity

2011-12-23

arxiv.org/abs/1112.5641v2

Physical Review D (Vol.85, No.6), 2012

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

39 pages, 4 figures, journal references added

Scientific paper

10.1103/PhysRevD.85.064009

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.

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