The equivalence problem in torsion theories of gravitation

Abstract

The basic problem of equivalence of gravitational fields in the framework of torsion theories of gravitation is solved. A coordinate-invariant description of the gravitational field is then presented. Explicit expressions for the dimensions of the group of transformations and its subgroup of isotropy are derived.

Riemann - Cartan spacetimes of Gödel type

“…To make apparent that the conditions for the local equivalence of RC manifolds follow from Cartan's approach to the equivalence problem, we shall first recall the definition of equivalence and then proceed by pointing out how Cartan's results [8] lead to the solution of the problem found in [13]. The basic idea is that if two Riemann-Cartan manifolds M and M are the same, they will define identical Lorentz frame bundles…”

“…In this article, in the light of the equivalence problem techniques for Riemann-Cartan space-times, as formulated by Fonseca-Neto et al [13] and embodied in the suite of computer algebra programs tclassi [14] - [16], we shall examine all Riemann-Cartan manifolds endowed with a Gödel-type metric (1.1), with a torsion polarized along the preferred direction defined by the rotation, and sharing the translational symmetries of g µν in (1.1).…”

“…The equivalence problem in torsion theories of gravitation (RC space-times), on the other hand, was only discussed recently [13]. Subsequently, an algorithm for checking the equivalence in TTG and a first working version of a computer algebra package (called tclassi) which implements this algorithm have been presented [14] - [16].…”

“…[8]) together with Cartan equations of structure for a manifold endowed with a nonsymmetric connection. The solution can be summarized as follows [13,16].…”

“…Two RC manifolds M and M are then said to be locally equivalent when there exists a local mapping F between the Lorentz frame bundles L(M) and L( M ) such that (see [13] and also Ehlers [25])…”