Teleparallel Energy-Momentum Distribution of Static Axially Symmetric Spacetimes

Abstract

This paper is devoted to discuss the energy-momentum for static axially symmetric spacetimes in the framework of teleparallel theory of gravity. For this purpose, we use the teleparallel versions of Einstein, Landau-Lifshitz, Bergmann and M$\ddot{o}$ller prescriptions. A comparison of the results shows that the energy density is different but the momentum turns out to be constant in each prescription. This is exactly similar to the results available in literature using the framework of General Relativity. It is mentioned here that M$\ddot{o}$ller energy-momentum distribution is independent of the coupling constant $λ$. Finally, we calculate energy-momentum distribution for the Curzon metric, a special case of the above mentioned spacetime.

14 pages, accepted for publication in Mod. Phys. Lett. A