(Received March 26, 1981)
In the translation gauge theory of gravitation, we give a general expression of the affine connexion coefficient satisfying the following conditions: (i) It is a function of the vierbien bkµ and of its first derivative bµk,ν. (ii) It is linear in bµk,ν. (iii) It satisfies the metricity condition. Our expression includes both of the connexion coefficients of the Riemann and Weitzenböck space-times as special ones, and hence, the space-time in the translation gauge theory is of Riemann-Cartan type. We fix the gravitational interaction of matter fields following Hayashi's method. The most general quadratic Lagrangian density of bkµ is represented in terms of the curvature scalar and of the torsion tensor. In the case of electromagnetic field interacting with gravitational field, it is pointed out that the torsion tensor can give rise to observable effects if the field strength Fµν of the electromagnetic field is given by Fµν=∇µAν-∇νAµ. Besides the electric charge of the matter field there is a charge which is associated both with the gravitational and electromagnetic fields. In the case of the electromagnetic and gravitational fields produced by a spherically symmetric massive charged matter, the effects of the torsion tensor appear in the post-Newtonian term in the gravitational potential and in the “post-Coulombian term” in the electric field strength. We point out the available experimental data in the astronomy impose no restriction on the connexion coefficient.
URL : http://ptp.ipap.jp/link?PTP/67/1107/
DOI : 10.1143/PTP.67.1107