Inhomogeneous Universe in f(T) Theory

Abstract

We obtain the equations of motions of the $f(T)$ theory considering the Lema\^itre-Tolman-Bondi's metric for a set of diagonal and non-diagonal tetrads. In the case of diagonal tetrads the equations of motion of the $f(T)$ theory impose a constant torsion or the same equations of the General Relativity, while in the case of non-diagonal set the equations are quite different from that obtained in GR. We show a simple example of an universe dominated by the matter for the two cases. The comparison of the mass in the non-diagonal case shows a sort of increased with respect to the diagonal one. We also perform two examples for the non-diagonal case. The first concerns a black hole solution of type Sshwarzschild which presents a temperature higher than that of Schwarzschild, and a black hole in a dust-dominated universe.