Firstorder formulation of teleparallel gravity and dual loop gravity
Abstract
There are at least two ways to encode gravity into geometry: Einstein's general theory of relativity (GR) for the metric tensor, and teleparallel gravity, where torsion as opposed to curvature encodes the dynamics of the gravitational degrees of freedom. The main purpose of the paper is to explore the relation between loop gravity and teleparallel gravity. We argue that these two formulations of gravity are related to two different discretizations of the EinsteinCartan action, which were studied recently in the literature. The first discretization leads to the loop gravity kinematical phase space where the zero torsion condition is enforced first and the other is the dual loop gravity kinematical phase space where curvature is imposed to vanish first. Our argument is based on the observation that the GR firstorder EinsteinCartan action can also be seen as a firstorder action for teleparallel gravity up to a boundary term. The results of our paper suggest that the dual loop gravity framework is a natural discretization of teleparallel gravity, whereas loop gravity is naturally related to the standard GR metric description.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 April 2020
 DOI:
 10.1088/13616382/ab7bb7
 arXiv:
 arXiv:1906.02801
 Bibcode:
 2020CQGra..37h5023D
 Keywords:

 teleparallel gravity;
 loop quantum gravity;
 dual loop quantum gravity;
 General Relativity and Quantum Cosmology
 EPrint:
 13 pages