Multimetric Finsler Geometry

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.

27 pages

References in corpus (9)

• Quantum Gravity at a Lifshitz Point
• Bipartite Riemann-Finsler geometry and Lorentz violation
• Modified Newton's gravity in Finsler Space as a possible alternative to dark matter hypothesis
• Finsler and Lagrange Geometries in Einstein and String Gravity
• Cosmological Finsler Spacetimes
• Mathematical foundations for field theories on Finsler spacetimes
• Relativistic kinetic gases as direct sources of gravity
• The kinetic gas universe
• On geodesics in space-times with a foliation structure: A spectral geometry approach

Cited by in corpus (5)

• Four-dimensional SO(3)-spherically symmetric Berwald Finsler spaces
• On the metrizability of $m$-Kropina spaces with closed null 1-form
• Birkhoff Theorem for Berwald Finsler spacetimes
• Modelling Cosmic Springs with Finsler and Generalised Finsler Geometries
• Quantum proper time: A Finsler space from entropy and purity