Symmetry in Cartan language for geometric theories of gravity

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, Weizenböck and Finsler spacetimes.

2 pages, no figures; to appear in the conference proceedings of the XIIth International Conference on Gravitation, Astrophysics and Cosmology, World Scientific Publishing Company