Multimetric Finsler Geometry

TL;DR

This paper introduces multimetric Finsler geometry, exploring its properties in arbitrary dimensions and explicitly deriving key equations and measures in the 2-dimensional case, inspired by bi-gravity theories.

Contribution

It develops the foundational aspects of multimetric Finsler geometry and provides explicit formulations for the 2D case, expanding geometric frameworks related to massive gravity.

Findings

Derived Cartan equations for 2D multimetric Finsler geometry

Explicitly calculated Holmes-Thompson measure in 2D

Analyzed properties of the geometry in arbitrary dimensions

Abstract

Motivated in part by the bi-gravity approach to massive gravity, we introduce and study the multimetric Finsler geometry. For the case of an arbitrary number of dimensions, we study some general properties of the geometry in terms of its Riemannian ingredients, while in the 2-dimensional case, we derive all the Cartan equations as well as explicitly find the Holmes-Thompson measure.