Teleparallel geometry with a single affine symmetry

Abstract

In teleparallel geometries, symmetries are represented by affine frame symmetries that constrain both the (co)frame basis and the spin-connection (which are the primary geometric objects). In this paper, we shall study teleparallel geometries with a single affine symmetry, utilizing the locally Lorentz covariant approach and adopting a complex null gauge. We first introduce an algorithm to study geometries with an affine frame symmetry, which consists of choosing coordinates adapted to the symmetry, constructing a canonical frame, and solving the equations describing the symmetry. All of the constraints on the geometry are determined in the case of a single affine symmetry, but there are additional constraints arising from the field equations for a given theory of teleparallel gravity. In particular, we find that in f(T) teleparallel gravity there will be severe constraints on the geometry arising from the antisymmetric part of the field equations.