The interactions between two classical spinning particles

Using an approximation method I consider the stationary axially symmetric solution of Einstein's equations for two spinning particles. In general there are two singularities. One represents a strut counteracting the gravitation of the particles, to which the spin-spin interaction makes a contribution. The other, called a torsion singularity, engenders a region with closed timelike curves. I conjecture that it represents a couple keeping the spins of the particles constant and thereby preventing an exchange of angular momentum. It vanishes (in the second approximation) when the angular momenta per unit mass of the particles are equal and opposite.