f(T) gravity and energy distribution in Landau–Lifshitz prescription

We investigate in this paper the Landau–Lifshitz energy distribution in the framework of f(T) theory view as a modified version of Teleparallel theory. From some important Teleparallel theory results on the localization of energy, our investigations generalize the Landau–Lifshitz prescription from the computation of the energy–momentum complex to the framework of f(T) gravity as it is done in the modified versions of General Relativity. We compute the energy density in the first step for three plane-symmetric metrics in vacuum. We find for the second metric that the energy density vanishes independently of f(T) models. We find that the Teleparallel Landau–Lifshitz energy–momentum complex formulations for these metrics are different from those obtained in General Relativity for the same metrics. Second, the calculations are performed for the cosmic string spacetime metric. It results that the energy distribution depends on the mass M and the radius r of cosmic string and it is strongly affected by the para...