2011/12/31 by Christian Pfeifer, Mattias N. R. Wohlfarth · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Classical mechanics #Computer science #Cosmology and Gravitation Theories #Einstein #Extension (predicate logic) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum gravity #Quantum mechanics #Theoretical physics #f(R) gravity #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.85.064009
published as Physical Review D (Vol.85, No.6), 2012 · 39 pages, 4 figures, journal references added
openalex publication_date 2012/03/08 · arxiv created 2012/03/09 · arxiv updated 2012/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.