Topological and physical effects of rotation and spin in the general relativistic theory of gravitation

Abstract

Interrelations of the intrinsic momentum (spin), rotation of material distributions, and intrinsic momentum of the gravitational field are investigated in the context of the general relativistic theory of gravitation involving the general relativity theory (GRT) and the Einstein-Cartan theory. It is demonstrated that the spin density vector of the gravitational field s _g ⁱ is equal to the rotor of the tetrad reference point ωⁱ=ɛ^iklm e _k ^(a) e_(a)l,m/2 to within the factor 1/κ (s _g ⁱ =ω/κc). It is demonstrated that the vector s _g ⁱ is proportional to the spin density vector of the gravitating field sⁱ (ω)=jc(Ψγⁱγ₅Ψ)/2 as well as the pseudovector of space-time torsion Qⁱ in the Einstein-Cartan theory, which in both cases induces a cubic nonlinearity of the spinor field. An expression for the energy-momentum density tensor of the eddy gravitational field is derived. It is also demonstrated that the free eddy gravitational field with polarized spin can form “mole holes.” An ideal fast-rotating self-gravitating fluid can cause a similar effect. The corresponding exact solutions of joint systems of the Einstein and rotating ideal fluid equations are presented.