Pseudo-Finsler spaces modeled on a pseudo-Minkowski space

Abstract

We adopt a vierbein formalism to study pseudo-Finsler spaces modeled on a pseudo-Minkowski space. We show that it is possible to obtain closed expressions for most of the geometric objects of the theory, including Berwald's curvature, Landsberg's tensor, Douglas' curvature, non-linear connection and Ricci scalar. These expressions are particularly convenient in computations since they factor the dependence on the base and the fiber. As an illustration, we study Lorentz-Finsler spaces modeled on the Bogoslovsky Lorentz-Minkowski space, and give sufficient conditions which guarantee the Berwald property. We then specialize to a recently proposed Finslerian pp-wave metric. Finally, the paper points out that non-trivial Berwald spaces have necessarily indicatrices which admit some non-trivial linear group of symmetries.

15 pages, no figures. Accepted by "Reports on Mathematical Physics"

References in corpus (10)

• Very Special Relativity
• General Very Special Relativity is Finsler Geometry
• xPerm: fast index canonicalization for tensor computer algebra
• The geometry of Minkowski spaces -- a survey. Part I
• Finsler pp-waves
• Raychaudhuri equation and singularity theorems in Finsler spacetimes
• The connections of pseudo-Finsler spaces
• Affine sphere relativity
• Affine sphere spacetimes which satisfy the relativity principle
• Monochromatic metrics are generalized Berwald

Cited by in corpus (6)

• Geodesic motion in Bogoslovsky-Finsler Spacetimes
• On the analyticity of static solutions of a field equation in Finsler gravity
• On the non metrizability of Berwald Finsler spacetimes
• Identifying Berwald Finsler Geometries
• Four-dimensional SO(3)-spherically symmetric Berwald Finsler spaces
• On the metrizability of $m$-Kropina spaces with closed null 1-form