Teleparallel Gravity: An Overview

A review of the teleparallel equivalent of general relativity is presented. It is emphasized that general relativity may be formulated in terms of the tetrad fields and of the torsion tensor, and that this geometrical formulation leads to alternative insights into the theory. The equivalence with the standard formulation in terms of the metric and curvature tensors takes place at the level of field equations. The review starts with a brief account of the history of teleparall...

Teleparallel gravity shares many qualitative features with general relativity, but differs from it in the following way: whereas in general relativity, gravitation is a manifestation of space-time curvature, in teleparallel gravity, spacetime is (always) flat. Gravitational effects in this theory arise due to spacetime torsion. It is often claimed that teleparallel gravity is an equivalent reformulation of general relativity. In this paper we question that view. We argue that...

An axiomatization of the so-called Teleparallel Equivalent to General Relativity is presented. A set of formal and semantic postulates are elaborated from where the physical meaning of various key concepts of the theory are clarified. These concepts include those of inertia, Lorentz and diffeomorphism invariance, and reference frame. It is shown that Teleparallel Gravity admits a wider representation of space-time than General Relativity, allowing to define properties of the ...

General relativity can be presented in terms of other geometries besides Riemannian. In particular, teleparallel geometry (i.e., curvature vanishes) has some advantages, especially concerning energy-momentum localization and its ``translational gauge theory'' nature. The standard version is metric compatible, with torsion representing the gravitational ``force''. However there are many other possibilities. Here we focus on an interesting alternate extreme: curvature and torsi...

After reminder some facts concerning general relativity ({\bf GR}) we pass to teleparallel gravity. We are confining the special model of the teleparallel gravity, which is popular recently, called {\it the teleparallel equivalent of general relativity} ({\bf TEGR}). We are finishing with conclusion and some general remarks.

The role played by torsion in gravitation is critically reviewed. After a description of the problems and controversies involving the physics of torsion, a comprehensive presentation of the teleparallel equivalent of general relativity is made. According to this theory, curvature and torsion are alternative ways of describing the gravitational field, and consequently related to the same degrees of freedom of gravity. However, more general gravity theories, like for example Ei...

In general relativity, the only dynamical field describing the gravitational interaction of matter, is the metric. It induces the causal structure of spacetime, governs the motion of physical bodies through its Levi-Civita connection, and mediates gravity via the curvature of this connection. While numerous modified theories of gravity retain these principles, it is also possible to introduce another affine connection as a fundamental field, and consider its properties - curv...

In the context of the teleparallel equivalent of general relativity, we show that the energy-momentum density for the gravitational field can be described by a true spacetime tensor. It is also invariant under local (gauge) translations of the tangent space coordinates, but transforms covariantly only under global Lorentz transformations. When the gauge gravitational field equation is written in a purely spacetime form, it becomes the teleparallel equivalent of Einstein's equ...

Teleparallel gravity, a gauge theory for the translation group, turns up as fully equivalent to Einstein's general relativity. In spite of this equivalence, it provides a whole new insight into gravitation. It breaks several paradigms related to the geometric approach of general relativity, and introduces new concepts in the description of the gravitational interaction. The purpose of this chapter is to explore some of these concepts, as well as discuss possible consequences ...

Due to its underlying gauge structure, teleparallel gravity achieves a separation between inertial and gravitational effects. It can, in consequence, describe the isolated gravitational interaction without resorting to the equivalence principle, and is able to provide a tensorial definition for the energy-momentum density of the gravitational field. Considering the conceptual conflict between the local equivalence principle and the nonlocal uncertainty principle, the replacem...