An anisotropic gravity theory

TL;DR

This paper investigates an anisotropic gravity model based on Finsler geometry, showing that in vacuum, its equations reduce to those of general relativity, indicating no observable anisotropic effects in vacuum conditions.

Contribution

It introduces a Finsler gravity action derived from an Einstein-Cartan-like Lagrangian and demonstrates that vacuum solutions align with general relativity.

Findings

Vacuum equations are independent of the observer section.

In vacuum, the metric reduces to a form independent of velocity variables.

The dynamics coincide with those of general relativity in vacuum.

Abstract

We study an action integral for Finsler gravity obtained by pulling back an Einstein-Cartan-like Lagrangian from the tangent bundle to the base manifold. The vacuum equations are obtained imposing stationarity with respect to any section (observer) and are well posed as they are independent of the section. They imply that in vacuum the metric is actually independent of the velocity variable so the dynamics becomes coincident with that of general relativity.