Teleparallel Gravity: An Overview

At the time it celebrates one century of existence, general relativity---Einstein's theory for gravitation---is given a companion theory: the so-called teleparallel gravity, or teleparallelism for short. This new theory is fully equivalent to general relativity in what concerns physical results, but is deeply different from the conceptual point of view. Its characteristics make of teleparallel gravity an appealing theory, which provides an entirely new way to think the gravit...

I consider the classical (i.e., non-relativistic) limit of Teleparallel Gravity, a relativistic theory of gravity that is empirically equivalent to General Relativity and features torsional forces. I show that as the speed of light is allowed to become infinite, Teleparallel Gravity reduces to Newtonian Gravity without torsion. I compare these results to the torsion-free context and discuss their implications on the purported underdetermination between Teleparallel Gravity an...

We review the book of Ruben Aldrovandi and Jose Geraldo Pereira about Teleparallel Gravity. Teleparallel Gravity is an alternative to General Relativity to describe the gravitational interaction. The difference between General Relativity and Teleparallel Gravity is the fact that General Relativity associates the curvature to the gravitational interaction, whereas in the Teleparallel Gravity the mathematical object associated to gravitational field is the torsion, whose field ...

According to the teleparallel equivalent of general relativity, curvature and torsion are two equivalent ways of describing the same gravitational field. Despite equivalent, however, they act differently: whereas curvature yields a geometric description, in which the concept of gravitational force is absent, torsion acts as a true gravitational force, quite similar to the Lorentz force of electrodynamics. As a consequence, the right-hand side of a spinless-particle equation o...

We give a pedagogical introduction into the field of (modified) teleparallel theories of gravity. Our presentation is fairly self-contained. In particular, we carefully explain the basic principles of metric-affine approaches to gravity. This contribution is based on our talk "Teleparallel gravity, its modifications, and the local Lorentz invariance" at the 9th Mathematical Physics Meeting: School and Conference on Modern Mathematical Physics in Belgrade, September 2017.

We analyze the relation between teleparallelism and local Lorentz invariance. We show that generic modifications of the teleparallel equivalent to general relativity will not respect local Lorentz symmetry. We clarify the reasons for this and explain why the situation is different in general relativity. We give a prescription for constructing teleparallel equivalents for known theories. We also explicitly consider a recently proposed class of generalized teleparallel theories...

Using the fact that teleparallel gravity allows a separation between gravitation and inertia, explicit expressions for the gravitational and the inertial energy-momentum densities are obtained. It is shown that, like all other fields of nature, gravitation alone has a tensorial energy-momentum density which in a general frame is conserved in the covariant sense. Together with the inertial energy-momentum density, they form a pseudotensor which is conserved in the ordinary sen...

In the framework of the teleparallel equivalent of general relativity, we study the dynamics of a gravitationally coupled electromagnetic field. It is shown that the electromagnetic field is able not only to couple to torsion, but also, through its energy-momentum tensor, to produce torsion. Furthermore, it is shown that the coupling of the electromagnetic field with torsion preserves the local gauge invariance of Maxwell's theory.

A class of theories of gravitation that naturally incorporates preferred frames of reference is presented. The underlying space-time geometry consists of a partial parallelization of space-time and has properties of Riemann-Cartan as well as teleparallel geometry. Within this geometry, the kinematic quantities of preferred frames are associated with torsion fields. Using a variational method, it is shown in which way action functionals for this geometry can be constructed. Fo...

We study the variational principle and derivation of the field equations for different classes of teleparallel gravity theories, using both their metric-affine and covariant tetrad formulations. These theories have in common that in addition to the tetrad or metric, they employ a flat connection as additional field variable, but differ by the presence of absence of torsion and nonmetricity for this independent connection. Besides the different underlying geometric formulation...