Metrizability of SO(3)-invariant connections: Riemann versus Finsler

Abstract

For a torsion-free affine connection on a given manifold, which does not necessarily arise as the Levi-Civita connection of any pseudo-Riemannian metric, it is still possible that it corresponds in a canonical way to a Finsler structure; this property is known as Finsler (or Berwald-Finsler) metrizability. In the present paper, we clarify, for 4-dimensional SO(3)-invariant, Berwald-Finsler metrizable connections, the issue of the existence of an affinely equivalent pseudo-Riemannian structure. In particular, we find all classes of SO(3)-invariant connections which are not Levi-Civita connections for any pseudo-Riemannian metric - hence, are non-metric in a conventional way - but can still be metrized by SO(3)-invariant Finsler functions. The implications for physics, together with some examples are briefly discussed.

22 pages

References in corpus (13)

• General Very Special Relativity is Finsler Geometry
• Planck-scale modified dispersion relations and Finsler geometry
• Realization of DSR-relativistic symmetries in Finsler geometries
• Classical-physics applications for Finsler $b$ space
• Light cones in Finsler spacetime
• Deformed relativity symmetries and the local structure of spacetime
• Mathematical foundations for field theories on Finsler spacetimes
• Relativistic kinetic gases as direct sources of gravity
• The Euler-Lagrange PDE and Finsler metrizability
• The kinetic gas universe
• Four-dimensional SO(3)-spherically symmetric Berwald Finsler spaces
• On the metrizability of $m$-Kropina spaces with closed null 1-form
• Finsler Geometry, Spacetime & Gravity -- From Metrizability of Berwald Spaces to Exact Vacuum Solutions in Finsler Gravity

Cited by in corpus (1)

• Berwald $m$-Kropina Spaces of Arbitrary Signature: Metrizability and Ricci-Flatness