An anisotropic gravity theory

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.