From a rigorous Finsler geometric perspective, we re-examine Holland’s Randers space theory of motion of an electron in flat Minkowski spacetime permeated with an electromagnetic field. Holland’s theory was motivated by analogy with plastic deformation and dislocation in Bravais crystals, through work of D. Bohm on Quantum Mechanics. We develop the anholonomic geometry of a Randers space using ...

Finsler geometry is an important extension of Riemann geometry, in which to each point the spacetime manifold arbitrary internal variable associated. Interesting geometries, with many physical applications, are Randers and Kropina type respectively. A subclass geometries represented by osculating spaces, a function base coordinates only. In one introduces Barthel connection, has remarkable prop...

In this work we study Randers spacetimes of Berwald type and analyze Pfeifer Wohlfarth's vacuum field equation Finsler gravity for class. We show that in case the is equivalent to vanishing Ricci tensor, analogously Einstein gravity. This implies considered Rutz's coincide scenario. also construct all exact solutions Berwald-Randers gravity, which turn out be composed a CCNV (covariantly consta...

Lorentz Violation is a common feature of Planck-scale phenomenology. We show that the symmetry of Randers spaces deduces a modified dispersion relation, which takes the quantum gravity effects into account. The counterparts of the Lorentz transformation in the Einstein’s Special Relativity are presented explicitly. The coordinate transformations are unitary and form a group. Generators and alge...

On a Finsler manifold (M,L), we consider the change L −→ L(x, y) = eL(x, y) + β(x, y), which we call a β-conformal change. This change generalizes various types of changes in Finsler geometry: conformal, C-conformal, h-conformal, Randers and generalized Randers changes. Under this change, we obtain an explicit expression relating the Cartan connection associated to (M,L) and the transformed Car...

Abstract The main result of this paper is an expression the flag curvature a submanifold Randers–Minkowski space $$({\mathscr {V}},F)$$ ( V , F ) in terms invariants related to its Zermelo data ( h , W ). More precisely...

In this paper we prove some results on the number of geodesics connecting two points or two submanifolds on a non-reversible complete Finsler manifold, in particular for complete Randers metrics. We apply the abstract results to the study of light rays and timelike geodesics with fixed energy on a standard stationary Lorentzian manifold.