Teleparallelism: fundamentals and applications

Abstract

The teleparallel equivalent of general relativity, which corresponds to a gauge theory for the translation group, has shown to provide an interesting approach to deal with several aspects of gravitation. We plan to develop further the foundations of this theory, as well as to reconsider some specific problems of gravitation as seen from the teleparallel point of view. We will be mainly interested in fundamental questions, like for example the inertia definition, or the quest for a tensorial expression for the energy-momentum density of gravity. On the other hand, there is today a general belief that special relativity, whose kinematics is governed by the Poincaré group, is not valid near the Planck scale. As a consequence, new kinematics has been studied which are known as doubly (or deformed) special relativity. Most of these models presuppose a violation of Lorentz symmetry. An alternative to these models is the deSitter special relativity, which presupposes a violation, not of Lorentz, but of the translation invariance. We plan to study the consequences of this violation for teleparallel gravity, as well as possible implications for quantum gravity. (AU)