Finsler geometry as a model for relativistic gravity

Abstract

We give an overview on the status and on the perspectives of Finsler gravity, beginning with a discussion of various motivations for considering a Finslerian modification of General Relativity. The subjects covered include Finslerian versions of Maxwell's equations, of the Klein-Gordon equation and of the Dirac equation, and several experimental tests of Finsler gravity.

16 pages, submitted to the proceedings volume of the conference `Geometric Foundations of Gravity' in Tartu 2017

References in corpus (7)

• The Confrontation between General Relativity and Experiment
• General Very Special Relativity is Finsler Geometry
• Planck-scale modified dispersion relations and Finsler geometry
• Riemann-Finsler geometry and Lorentz-violating kinematics
• Light cones in Finsler spacetime
• Finsler-type modification of the Coulomb law
• Radar orthogonality and radar length in Finsler and metric spacetime geometry

Cited by in corpus (39)

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• Mathematical foundations for field theories on Finsler spacetimes
• 3+1 Formulation of the Standard-Model Extension Gravity Sector
• Foundations of Finsler spacetimes from the Observers' Viewpoint
• Searches for beyond-Riemann gravity
• Redshift in Finsler spacetimes
• Homogeneously Modified Special Relativity (HMSR) -- A new possible way to introduce an isotropic Lorentz Invariance Violation in particle Standard Model
• Neutrino Oscillations and Lorentz Invariance Violation
• Geodesic motion in Bogoslovsky-Finsler Spacetimes
• On the non metrizability of Berwald Finsler spacetimes
• Finslerian wormhole solution in the framework of modified gravity
• Phenomenological Effects of CPT and Lorentz Invariance Violation in Particle and Astroparticle Physics
• Broken Scale Invariance, Gravity Mass, and Dark Energy in Modified Einstein Gravity with Two Measure Finsler Like Variables
• Thermodynamics of $f(R)$ Gravity with Disformal Transformation
• On the Jacobi metric for a general Lagrangian system
• Predictions of Ultra-High Energy Cosmic Ray Propagation in the Context of Homogeneously Modified Special Relativity
• Finsler gravitational waves of $(\alpha ,\beta )$-type and their observational signature
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• A Cosmological Unicorn Solution to Finsler Gravity
• Spontaneous and Explicit Spacetime Symmetry Breaking in Einstein-Cartan Theory with Background Fields
• Four-dimensional SO(3)-spherically symmetric Berwald Finsler spaces
• Harmonic functions and gravity localization
• On the metrizability of $m$-Kropina spaces with closed null 1-form
• Physical dimensions/units and universal constants: their invariance in special and general relativity
• On the significance of the stress-energy tensor in Finsler spacetimes
• Metrizability of SO(3)-invariant connections: Riemann versus Finsler
• From kinetic gases to an exponentially expanding universe - The Finsler-Friedmann equation
• Geometric Description of Schrödinger Equation in Finsler and Funk Geometry
• Electromagnetic and gravitational interactions from Lagrangian mechanics
• Characteristic tensors for almost Finsler manifolds
• DISIMb(2) Local Relativistic Symmetry and Finslerian Extension of the Theory of Relativity
• Finslerian representation of the Maxwell equations
• On Finslerian extension of special relativity
• On the pseudo-Riemann's quartics in Finsler's geometry
• Numerical Modelling of Satellite Downlink Signals in a Finslerian-Perturbed Schwarzschild Spacetime