The teleparallel equivalent of general relativity

TL;DR

This paper reviews the teleparallel formulation of general relativity, highlighting its use of tetrad fields and torsion, and discusses how it provides alternative insights and definitions of gravitational energy-momentum.

Contribution

It presents a comprehensive review of the teleparallel equivalent of general relativity, emphasizing its geometrical formulation and physical implications.

Findings

Equivalence with standard GR at the level of field equations.

Energy, momentum, and angular momentum are defined as surface integrals.

The phase space quantities satisfy the Poincaré algebra.

Abstract

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 teleparallel theories of gravity. Then the ordinary interpretation of the tetrad fields as reference frames adapted to arbitrary observers in space-time is discussed, and the tensor of inertial accelerations on frames is obtained. It is shown that the Lagrangian and Hamiltonian field equations allow to define the energy, momentum and angular momentum of the gravitational field, as surface integrals of the field quantities. In the phase space of the theory, these quantities satisfy the algebra of the Poincar\'{e} group.