On Torsion Axial Vector and gravitational Energy in Lewis-Papapetrou Space-Time in the Theory of Teleparallel Gravity

The teleparallel version of Lewis-Papapetrou space-time is investigated. For this space-time the true discussion of the geometric and physical properties is given. We show that the value of space-like torsion-axial vector does not depend on the choice of tetrad field. Consequently, the spin procession of the Dirac particle and the corresponding Hamiltonian do. The energy and momentum densities for such space-time are calculated. We show that when choosing two sets of tetrad fields the dependence and independence of the aforementioned quantities on the tetrad field depend on the Lorentz factor, which links the two sets of tetrad fields.