Geometrically contracted structure in teleparallel $f(T)$ gravity

TL;DR

This paper explores five-dimensional thick branes in teleparallel $f(T)$ gravity, showing how polynomial $f(T)$ profiles can produce internal structures and stable, compact-like matter configurations, analyzed via Configurational Entropy.

Contribution

It introduces polynomial $f(T)$ profiles that generate internal structures and stability analysis of branes using Configurational Entropy in teleparallel gravity.

Findings

Polynomial $f(T)$ profiles can produce brane splitting and internal structures.

Stable, compact-like matter configurations are identified.

Configurational Entropy effectively determines the most stable $f(T)$ profiles.

Abstract

In the teleparallel $f(T)$ gravity scenario, we consider a five-dimensional thick brane. This scenario is interesting because this theory can provide explanations for inflation, radiation, and dark matter under certain conditions. It is convenient to assume, for our study, a polynomial profile of the function $f(T)$. Indeed, some polynomial profiles can produce internal structures for which a brane splitting occurs. For functions $f(T)$ with this capability, geometrically contracted matter field configurations are obtained. These contractions of the matter field for the profiles of $f(T)$ reproduce compact-like settings. To complement the study, we analyze the stability of the brane using the concept of Configurational Entropy (CE). The CE arguments are interesting because they tell us the most stable and likely configurations from the brane in this gravitational background. Therefore, we can indicate the best profile of the function $f(T)$.