Berwald spacetimes and very special relativity

Abstract

In this work we study Berwald spacetimes and their vacuum dynamics, where the latter are based on a Finsler generalization of the Einstein's equations derived from an action on the unit tangent bundle. In particular, we consider a specific class of spacetimes which are non-flat generalizations of the very special relativity (VSR) line element, to which we refer as very general relativity (VGR). We derive necessary and sufficient conditions for the VGR line element to be of Berwald type. We present two novel examples with the corresponding vacuum field equations: a Finslerian generalization of vanishing scalar invariant (VSI) spacetimes in Einstein's gravity as well as the most general homogeneous and isotropic VGR spacetime.

arXiv comment17 pages, example section updated, journal references added

References in corpus (44)

• Gravity, Lorentz Violation, and the Standard Model
• Very Special Relativity
• General Very Special Relativity is Finsler Geometry
• Planck-scale modified dispersion relations and Finsler geometry
• Riemann-Finsler geometry and Lorentz-violating kinematics
• Finsler geometric extension of Einstein gravity
• The General Very Special Relativity in Finsler Cosmology
• Causal structure and electrodynamics on Finsler spacetimes
• All spacetimes with vanishing curvature invariants
• Resembling dark energy and modified gravity with Finsler-Randers cosmology
• Classical kinematics for Lorentz violation
• Principles of Einstein-Finsler Gravity and Perspectives in Modern Cosmology
• Exact solution of vacuum field equation in Finsler spacetime
• Observable effects in a class of spherically symmetric static Finsler spacetimes
• Realization of DSR-relativistic symmetries in Finsler geometries
• Geometry of physical dispersion relations
• Finsler geometry as a model for relativistic gravity
• Implications of a Stochastic Microscopic Finsler Cosmology
• Modified Friedmann model in Randers-Finsler space of approximate Berwald type as a possible alternative to dark energy hypothesis
• Classical Lagrangians and Finsler structures for the nonminimal fermion sector of the Standard-Model Extension
• Linear pre-metric electrodynamics and deduction of the light cone
• Finsler-Randers Cosmology: dynamical analysis and growth of matter perturbations
• Finslerian spaces possessing local relativistic symmetry
• On a Possibility of Phase Transitions in the Geometric Structure of Space-Time
• Geodesics and the magnitude-redshift relation on cosmologically symmetric Finsler spacetimes
• Finsler pp-waves
• A class of anisotropic (Finsler-) space-time geometries
• Deformed relativity symmetries and the local structure of spacetime
• Finsler metrics and relativistic spacetimes
• Gyratonic pp-waves and their impulsive limit
• Propagation of light in area metric backgrounds
• The connections of pseudo-Finsler spaces
• Modified Einstein and Finsler Like Theories on Tangent Lorentz Bundles
• Finslerian MOND vs. observations of Bullet Cluster 1E0657-558
• Rainbows without unicorns: Metric structures in theories with Modified Dispersion Relations
• Observers' measurements in premetric electrodynamics I: Time and radar length
• On singular generalized Berwald spacetimes and the equivalence principle
• Geometrical Models of the Locally Anisotropic Space-Time
• Cosmic magnetization in curved and Lorentz violating space-times
• Kinetic Energy and Angular Momentum of Free Particles in the Gyratonic pp-Waves Space-times
• Non-metric fluid dynamics and cosmology on Finsler spacetimes
• Special coordinate systems in pseudo-Finsler geometry and the equivalence principle
• Anisotropic power spectrum and the observed low-l power in PLANCK CMB data
• On the History of Geometrization of Space-time: From Minkowski to Finsler Geometry

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• Mathematical foundations for field theories on Finsler spacetimes
• Foundations of Finsler spacetimes from the Observers' Viewpoint
• Redshift in Finsler spacetimes
• Geodesic motion in Bogoslovsky-Finsler Spacetimes
• The kinetic gas universe
• On the analyticity of static solutions of a field equation in Finsler gravity
• Phenomenological Effects of CPT and Lorentz Invariance Violation in Particle and Astroparticle Physics
• Randers pp-waves
• Identifying Berwald Finsler Geometries
• Finsler gravitational waves of $(\alpha ,\beta )$-type and their observational signature
• The Einstein-Hilbert-Palatini formalism in Pseudo-Finsler Geometry
• A Cosmological Unicorn Solution to Finsler Gravity
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Anisotropic conformal invariance of lightlike geodesics in pseudo-Finsler manifolds
• Geometry of weighted Lorentz-Finsler manifolds II: A splitting theorem
• On the metrizability of $m$-Kropina spaces with closed null 1-form
• The Finsler spacetime condition for (α,β)-metrics and their isometries
• Lorentz Violation in Finsler Geometry
• Cosmological Landsberg Finsler spacetimes
• From Barthel Randers Kropina Geometries to the Accelerating Universe: A Brief Review of Recent Advances in Finslerian Cosmology
• On the significance of the stress-energy tensor in Finsler spacetimes
• Energy-momentum and angular-momentum of a gyratonic pp-waves spacetime
• Berwald $m$-Kropina Spaces of Arbitrary Signature: Metrizability and Ricci-Flatness
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations
• Fixed energy solutions to the Euler-Lagrange equations of an indefinite Lagrangian with affine Noether charge
• Finslerian geometrodynamics