Teleparallel equivalent of the Kaluza-Klein theory

Abstract

Relying upon the equivalence between a gauge theory for the translation group and general relativity, a teleparallel version of the original Kaluza-Klein theory is developed. In this model, only the internal space (fiber) turns out to be five dimensional, spacetime being kept always four dimensional. A five-dimensional translational gauge theory is obtained which unifies, in the sense of Kaluza-Klein theories, gravitational and electromagnetic interactions. 04.50.+h; 12.10.-g

Conservation laws in the teleparallel theory of gravity

“…[19], related to T 2 theories in U 4 , are encouraging. Among various successful applications of the teleparallel approach, one should mention a pure tensorial proof of the positivity of energy in GR [20], a transparent introduction of Ashtekar's complex variables [21], and a formulation of a five-dimensional teleparallel equivalent of the Kaluza-Klein theory [22]. Although quantum properties of PGT are in general not so attractive [23,24], the related behavior in the specific case of the teleparallel theory might be better [25,26], and should be further explored.…”

Reconstructions of f(T) gravity from entropy-corrected holographic and new agegraphic dark energy models in power-law and logarithmic versions

“…For the unusual character of these translations, any gauge theory with these translations is different from the usual gauge theory in many ways, mostly in the background of a tetrad field, whereas this field is used to define a linear Weitzenbock connection, presenting torsion without curvature. For the details of this gravity theory see the review [60]. We consider here how to generalize the telepar-…”

Teleparallel conformal invariant models induced by Kaluza–Klein reduction

“…Teleparallelism in the KK scenario has been discussed in [16][17][18][19][20][21]. In this study, we consider the high dimensional gravity theory based on the analogous form to (1.1) in the four dimensional NGR theory.…”