Finlser geometric extension of Einstein gravity

TL;DR

This paper introduces a Finsler spacetime formalism extending Einstein gravity, providing a non-metric geometric framework that supports causality, light propagation, and dynamic field theories in physics.

Contribution

It develops a rigorous definition of Finsler spacetimes and formulates a framework for physical observers and field theories within this extended geometric setting.

Findings

Finsler spacetimes support well-defined causality.

Light propagates on a non-trivial null structure.

Field theories can be formulated dynamically in Finsler geometry.

Abstract

We present our Finsler spacetime formalism which extends the standard formulation of Finsler geometry to be applicable in physics. Finsler spacetimes are viable non-metric geometric backgrounds for physics; they guarantee well defined causality, the propagation of light on a non-trivial null structure, a clear notion of physical observers and the existence of physical field theories determining the geometry of space-time dynamically in terms of an extended gravitational field equation. Here we give the precise definition of Finsler spacetimes and the notion of well-defined observers, their measurements, the transformations between them and how to formulate action based field theories.