Kinematics of the internal space associated with the TEGR

TL;DR

This paper explores the internal space kinematics in TEGR, revealing that the gauge symmetry may extend beyond the Poincaré group, with implications for understanding gravity's geometric structure.

Contribution

It introduces a generalized internal symmetry group in TEGR by decomposing tetrad components, extending the traditional Poincaré symmetry to a broader kinematical group.

Findings

The internal space symmetry group can be a generalization of the Poincaré group.

Decomposition of tetrad components influences the recovered symmetry group.

The internal space of gravity aligns with the physical space at a local level.

Abstract

In the context of Teleparallel Equivalent of General Relativity - TEGR - we have obtained, through the second kind gauge transformations, the most fundamental transformations, namely, the first kind ones. We show that considering the possibility of decomposing the components of the tetrad field as a trivial part plus some potential besides the usual translational and Lorentz potentials, there is also the possibility that the symmetry group of internal space be a generalization of the Poincar\'e group. Still in the analysis of transformations in the internal space, we saw that for the case in which the decomposition of the tetrad field components includes only a trivial part plus a translational potential, we are able to recover just the translational group. Moreover, the internal space of gravity must be the very physical space - on a local scale - in such a way that the gauge symmetry group is the kinematical group of the physical space itself. This group was obtained, and seems to generalize the Poincar\'e group.