Killing vectors of Schwarzschild space-times in teleparallel equivalent of general relativity

Abstract

We derive three different solutions in the framework of the teleparallel equivalent of general relativity (TEGR). We apply the energy-momentum tensor to calculate energy, irreducible mass, spatial momentum and angular-momentum associated with these solutions. We obtain anomalous physical results therefore, we calculate the Killing vectors using the definition of the Lie derivative.

A Note on Classification of Cylindrically Symmetric Non-static Space–Times According to Their Teleparallel Killing Vector Fields in the Teleparallel Theory of Gravitation

“…From the present work, it can be concluded that torsion has a stronger effect on the spacetime than curvature, as torsion produces at least one or at the most four more conservation laws. It is important to mention here that the significance of Killing symmetry in the teleparallel theory is quite clear because the teleparallel Killing vector fields can be studied to compare the results of energy, momentum, and angular momentum in both teleparallel and general relativity theories [13,17].…”