Symmetry in Cartan language for geometric theories of gravity

TL;DR

This paper introduces a new definition of symmetry vector fields in Cartan geometric frameworks and demonstrates its consistency with traditional symmetry concepts across various gravity-related spacetime models.

Contribution

It provides a unified Cartan geometric approach to symmetries in different gravity theories, aligning with established notions.

Findings

The new symmetry definition agrees with classical notions in affine, Riemann-Cartan, Riemannian, Weizenböck, and Finsler geometries.

The approach offers a consistent way to analyze symmetries in diverse spacetime models.

It bridges Cartan geometry with traditional symmetry concepts in gravity theories.

Abstract

We present a recent definition of symmetry generating vector fields on manifolds equipped with a first-order reductive Cartan geometry. We apply this definition to a number of spacetime geometries used in gravity theories and show that it agrees with the usual notions of symmetry of affine, Riemann-Cartan, Riemannian, Weizenb\"ock and Finsler spacetimes.