Finsler spacetimes and gravity

TL;DR

This paper explores Finsler geometry as a generalized framework for spacetime, defining causality, observers, and field theories, and extends Einstein's equations to this Finslerian context.

Contribution

It introduces a consistent definition of Finsler spacetimes with causality and observer concepts, and formulates a dynamic extension of Einstein's equations within this geometry.

Findings

Defined a well-structured notion of causality in Finsler spacetimes

Provided a geometric background suitable for field theories

Extended Einstein equations to Finsler geometry

Abstract

We consider the geometry of spacetime based on a non-metric, Finslerian, length measure, which, in terms of physics, represents a generalized clock. Our defnition of Finsler spacetimes ensure a well defined notion of causality, a precise description of observers and a geometric background for field theories. Moreover we present our Finsler geometric extension of the Einstein equations, which determine the geometry of Finsler spacetimes dynamically.