Spaces with flat symmetry in poincar� gauge theory of gravity

Abstract

A Taub space is considered in the Poincare gauge theory of gravity. It is shown that the torsion tensor has four nonvanishing components, which can be split into two independent pairs S010, S011, and S230, S231. The analysis of the gravitational field equations leads to the conclusion that in this case only a flat space-time with torsion is possible, and that its metric coefficients and the components of the torsion tensor are described by a wave equation.