Torsion-induced spin precession

We investigate the motion of a spinning test particle in a spatially-flat FRW-type space-time in the framework of the Einstein–Cartan theory. The space-time has a torsion arising from a spinning fluid filling the space-time. We show that, for spinning particles with non-zero transverse spin components, the torsion induces a precession of the particle spin around the direction of the spin of the fluid. We also show that a charged spinning particle moving in a torsion-less spatially-flat FRW space-time in the presence of a uniform magnetic field undergoes a precession of a different character.     

A singularity free solution of the Maxwell-Einstein equations

It is found that the massless charged particle permanently at rest at the origin of spherical polar coordinates in Lovelock's interpretation [1] of Robinson's solution of the Einstein-Maxwell equations [2] will repel all charged test particles, irrespective of the sign of their charges. By a global embedding of the space-time in a flat 6-space we find an absence of singularities where point-charges or point-masses might be located. With the use of the Newman-Penrose method of spin-coefficients [6] it is shown that all the Robinson solutions [2] represent constant electromagnetic fields.     

Magnetohydrodynamics in a Riemann-Cartan space-time

By assuming that Maxwell's electromagnetic field equations are valid in a Riemann-Cartan space-time and by using a set of rules to transform from Riemannian kinematics to Riemann-Cartan kinematics, the kinematic aspects of magnetohydrodynamics in a Riemann-Cartan space-time are examined. If the electric conductivity of the fluid is infinite, then the magnetic field conservation laws still hold, but torsion affects the physical interpretation of the equation for proper charge density. A result, based on the Ricci identity foru _a and the first Bianchi identity, and describing differential rotation of a charged fluid in a Riemann space-time, is extended to a Riemann-Cartan space-time. The kinematic role played by torsion in this result is examined.     

U(4) spin gauge theory over a Riemann-Cartan space-time

A spin gauge theory based on the groupU(4) is investigated in a general relativistic context including the possibility of nonzero torsion. The language of Clifford bundles over a space-time with metric and metric compatible torsion is used as a convenient tool for the study of fields defined on space-time possessing Clifford multiplication properties. A Dirac-type representation is investigated in detail and the geometric implications for spin gauge theory are pointed out.     

Unified Field Theoretical Models from Generalized Affine Geometries II

The space-time structure of the new Unified Field Theory presented in previous reference (Int. J. Theor. Phys. 49:1288–1301, 2010) is analyzed from its SL(2C) underlying structure in order to make precise the notion of minimal coupling. To this end, the framework is the language of tensors and particularly differential forms and the condition a priory of the existence of a potential for the torsion is relaxed. We shown trough exact cosmological solutions from this model, where the geometry is Euclidean R⊗O ₃∼R⊗SU(2), the relation between the space-time geometry and the structure of the gauge group. Precisely this relation is directly connected with the relation of the spin and torsion fields. The solution of this model is explicitly compared with our previous ones and we find that: (i) the torsion is not identified directly with the Yang Mills type strength field, (ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact lead the identification between derivatives of the scale factor a(τ) with the components of the torsion in order to allows the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), (iii) this compatibility condition precisely mark the fact that local gauge covariance, coordinate independence and arbitrary space time geometries are harmonious concepts and (iv) of two possible structures of the torsion the “tratorial” form (the only one studied here) forbids wormhole configurations, leading only, cosmological instanton space-time in eternal expansion.     

The radial force on a charged particle in superimposed magnetic fields on Schwarzschild spacetime

Following the approach of optical reference geometry we derive the expression for the total force in the radial direction acting on a charged particle in magnetic fields superimposed on the static Schwarzschild background and show the possible existence of bound orbits for particles in the field of ultra compact objects at distancesr?3m wherein the Lorentz force counterbalances both the gravitational and centrifugal forces.     

On unified field theories,dynamical torsion and geometrical models: II

We analyze in this letter the same space-time structure as that presented in our previous reference (Part. Nucl., Lett. 2010. V. 7, No. 5, P. 299–307), but relaxing now the condition a priori of the existence of a potential for the torsion. We show through exact cosmological solutions from this model, where the geometry is Euclidean R ⊗ O ₃ ∼ R ⊗ SU(2), the relation between the space-time geometry and the structure of the gauge group. Precisely this relation is directly connected with the relation between the spin and torsion fields. The solution of this model is explicitly compared with our previous ones and we find that: (i) the torsion is not identified directly with the Yang-Mills type strength field, (ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact leads to the identification between derivatives of the scale factor with the components of the torsion in order to allow the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), and (iii) of two possible structures of the torsion the “tratorial” form (the only one studied here) forbids wormhole configurations, leading only to cosmological space-time solution in eternal expansion.