ON THE GRAVITATIONAL ENERGY–MOMENTUM VECTOR IN f(T) THEORIES

Abstract

This work is devoted to present and analyze an expression for the gravitational energy–momentum vector in the context of f(T) theories through field equations. Such theories are the analogous counterpart of the well-known f(R) theories, except using torsion instead of curvature. We obtain a general expression for the gravitational energy–momentum vector in this framework. Using the hypothesis of the isotropy of spacetime, we find the gravitational energy for a closed universe, since construction of real tetrads that do not constrain the functional form of the Lagrangian density was not possible for an open universe. Thus, we find a vanishing gravitational energy for the tetrad that we have used.