torsion. Disinclinations correspond to curvature, which is why they are left out. The torsion, i.e., the translational field strength of Teleparallel Gravity (or the translational "curvature"), is gauge invariant. Of course, we can always choose the gauge where is zero everywhere (a problem though; is an affine space and also a fiber and so, we have to define the origin on a point by point basis, but this can always be done arbitrarily) and this leads us back to the theory where the tetrad is fundamental. Teleparallelism refers to any theory of gravitation based upon this framework. There is a particular choice of the action which makes it exactly equivalent to general relativity, but there are also other choices of the action which are not equivalent to GR. In some of these theories, there is no equivalence between inertial and gravitational masses. Unlike GR, gravity is not due to the curvature of spacetime. It is due to the torsion. Non-gravitational contexts There exists a close analogy of geometry of spacetime with the structure of defects in crystal. Dislocations are represented by torsion, disclinations by curvature. These defects are not independent of each other. A dislocation is equivalent to a disclination-antidisclination pair, a disclination is equivalent to a string of dislocations. This is the basic reason why Einstein's theory based purely on curvature can be rewritten as a teleparallel theory based only on torsion. There exists, moreover, infinitely many ways of rewriting Einstein's theory, depending on how much of the curvature one wants to reexpress in terms of torsion, the teleparallel theory being merely one specific version of these. A further application of teleparallelism occurs in quantum field theory, namely, two-dimensional non-linear sigma models with target space on simple geometric manifolds, whose renormalization behavior is controlled by a Ricci flow, which includes torsion. This torsion modifies the Ricci tensor and hence leads to an infrared fixed point for the coupling, on account of teleparallelism ("geometrostasis"). See also Classical theories of gravitation Gauge gravitation theory References Further reading External links Selected Papers on Teleparallelism, translated and edited by D. H. Delphenich Teleparallel Structures and Gravity Theories by Luca Bombelli History of physics Theories of gravity