Berwald spacetimes and very special relativity

TL;DR

This paper explores Berwald spacetimes within Finsler geometry, focusing on vacuum solutions and a generalization of very special relativity, introducing new examples and conditions for these spacetimes to be of Berwald type.

Contribution

It provides the first analysis of Berwald spacetimes in the context of Finslerian generalizations of Einstein's equations, especially for very general relativity models.

Findings

Derived conditions for VGR line elements to be Berwald

Presented a Finslerian generalization of VSI spacetimes

Constructed the most general homogeneous and isotropic VGR spacetime

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.