On singular generalized Berwald spacetimes and the equivalence principle

TL;DR

This paper introduces singular generalized Finsler and Berwald spacetimes, explores their relevance to classical gravity, and constructs examples including flat and non-flat models, discussing their physical implications and Einstein equations.

Contribution

It presents a new framework for singular generalized Berwald spacetimes and provides methods to construct explicit examples at different levels of generality.

Findings

Constructed flat singular generalized Berwald spacetimes.

Presented non-flat generalized Berwald spacetimes and discussed Einstein equations.

Argued for a small cosmological constant in these models.

Abstract

The notion of singular generalized Finsler spacetime and singular generalized Berwald spacetime are introduced and their relevance for the description of classical gravity discussed. A method to construct examples of such generalized Berwald spacetimes is sketched. The method is applied at two different levels of generality. First, a class of flat, singular generalized Berwald spacetimes is obtained. Then in an attempt of further generalization, a class of non-flat generalized Berwald spacetimes is presented and the associated Einstein field equations are discussed. In this context, an argument in favour of a small value of the cosmological constant is given. The physical significance of the models is briefly discussed in the last section.