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.

Latex, 15 pages. v2: we fixed some typos and added two more appendices with proofs of formulas used in the work. To appear in the topical volume `Singularity theorems, causality, and all that (SCRI21)' https://link.springer.com/collections/hjjgajaagg

References in corpus (3)

• Mathematical foundations for field theories on Finsler spacetimes
• The Einstein-Hilbert-Palatini formalism in Pseudo-Finsler Geometry
• On the significance of the stress-energy tensor in Finsler spacetimes

Cited by in corpus (4)

• Four-dimensional SO(3)-spherically symmetric Berwald Finsler spaces
• On the metrizability of $m$-Kropina spaces with closed null 1-form
• Cosmological Landsberg Finsler spacetimes
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations