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

TL;DR

This paper explores the geometric and physical properties of Lewis-Papapetrou space-time in teleparallel gravity, focusing on torsion, spin procession, and energy-momentum densities, and how these depend on tetrad choices.

Contribution

It provides a detailed analysis of torsion axial vector and energy-momentum in teleparallel Lewis-Papapetrou space-time, highlighting tetrad dependence and invariance.

Findings

Torsion axial vector is independent of tetrad choice.

Energy and momentum densities depend on the Lorentz factor between tetrad sets.

Spin procession and Hamiltonian are unaffected by tetrad choice.

Abstract

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.