THE EQUIVALENCE PROBLEM IN TELEPARALLEL GRAVITY

Abstract

The teleparallel equivalent of general relativity (TEGR) is an alternative formulation of Einstein's equations in the framework of Riemann-Cartan spacetimes. The gravitational field can be described either by the curvature of the torsion-free connection of general relativity (GR) or by the torsion of the curvature-free connection of the TEGR. Both in GR and TEGR the freedom in the choice of coordinates gives rise to the equivalence problem of deciding whether two solutions of the field equations are the same. This problem is solved by means of a invariant description of the gravitational field. We investigate whether the equivalence between GR and TEGR also holds at the level of these invariant descriptions. We show that the GR description assures equivalence in TEGR only in very special situations. These results are illustrated on teleparallel spacetimes with torsion and Gödel metric.