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

TL;DR

This paper extends the Landau-Lifshitz energy-momentum complex to $f(T)$ gravity, analyzing energy distribution for specific spacetimes and revealing dependence on model parameters and cosmic string mass.

Contribution

It generalizes the Landau-Lifshitz energy distribution approach to $f(T)$ gravity, providing new insights into energy localization in modified teleparallel theories.

Findings

Energy density vanishes for one vacuum metric, consistent with literature.

Energy distribution in cosmic string spacetime depends on string mass and $f(T)$ model parameters.

Results align with previous studies, validating the generalized approach.

Abstract

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. These metrics provide results in perfect agreement with those mentioned in literature. In the second step the calculations are performed for the Cosmic String Spacetime metric. It results that the energy distribution depends on the mass $M$ of cosmic string and it is strongly affected by the parameter of the considered $f (T)$ quadratic model.