An exact solution of the Einstein-Cartan field equations

The exact solution of Einstein-Cartan field equations is obtained for an artificial fluid with radially polarized spins, spherically symmetric and under static condition; the energy-momentum metric tensor is taken as zero. The gravitational dynamics is studied for various intensities of torsion (or fluid spin), through the analysis of motion of spinless test particles; in particular, for vanishing torsion we reobtain the Schwarzschild solution. The gravitational effects related to torsion are found sometimes attractive, sometimes repulsive, depending on the value of spin density and on the position and velocity of the test particle. (Author)