Inhomogeneous Universe in f(T) Theory

TL;DR

This paper explores the equations of motion in f(T) gravity using Lemaître-Tolman-Bondi metrics, revealing differences between diagonal and non-diagonal tetrads and their implications for cosmological and black hole solutions.

Contribution

It derives and compares the equations of motion for f(T) gravity with different tetrad choices and examines their effects on cosmological models and black hole solutions.

Findings

Diagonal tetrads lead to equations similar to General Relativity.

Non-diagonal tetrads produce distinct equations, affecting mass and black hole properties.

Black holes in non-diagonal f(T) gravity can have higher temperatures.

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.