Finsler metrics and relativistic spacetimes

Abstract

Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other parts of Physics.

15 pages, v2: Final version with a new last section of conclusions and minor modifications, to appear in International Journal of Geometric Methods in Modern Physics, in the Special Issue for the XXII IFWGP Evora DOI: 10.1142/S0219887814600329

References in corpus (8)

• Riemann-Finsler geometry and Lorentz-violating kinematics
• The General Very Special Relativity in Finsler Cosmology
• Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry
• Bipartite Riemann-Finsler geometry and Lorentz violation
• Classical kinematics for Lorentz violation
• Modified Friedmann model in Randers-Finsler space of approximate Berwald type as a possible alternative to dark energy hypothesis
• Cyclic and Ekpyrotic Universes in Modified Finsler Osculating Gravity on Tangent Lorentz Bundles
• Critical Remarks on Finsler Modifications of Gravity and Cosmology by Zhe Chang and Xin Li

Cited by in corpus (26)

• On the definition and examples of cones and Finsler spacetimes
• Finsler-like structures from Lorentz-breaking classical particles
• Classical kinematics and Finsler structures for nonminimal Lorentz-violating fermions
• Geodesics and the magnitude-redshift relation on cosmologically symmetric Finsler spacetimes
• Finsler pp-waves
• Berwald spacetimes and very special relativity
• Wind Finslerian structures: from Zermelo's navigation to the causality of spacetimes
• Standard static Finsler spacetimes
• Foundations of Finsler spacetimes from the Observers' Viewpoint
• Analysis of birefringence and dispersion effects from spacetime-symmetry breaking in gravitational waves
• On the analyticity of static solutions of a field equation in Finsler gravity
• Applications of the Schwarzschild-Finsler-Randers model
• Randers pp-waves
• Finsler gravitational waves of $(\alpha ,\beta )$-type and their observational signature
• Volume forms for time orientable Finsler spacetimes
• On the metrizability of $m$-Kropina spaces with closed null 1-form
• Nonperturbative Lorentz Violation and Field Quantization
• Physical interpretation of large Lorentz violation via Weyl semimetals
• Generally covariant $N$-particle dynamics
• On the significance of the stress-energy tensor in Finsler spacetimes
• Conformal maps between pseudo-Finsler spaces
• Anisotropic Wavefronts and Laguerre Geometry
• Lightlike hypersurfaces and time-minimizing geodesics in cone structures
• Electromagnetic and gravitational interactions from Lagrangian mechanics
• Fixed energy solutions to the Euler-Lagrange equations of an indefinite Lagrangian with affine Noether charge
• Gauge-covariant Raychaudhuri dynamics for spin-nondegenerate Lorentz-violating congruences