Thick string-like braneworlds in f(T) gravity

TL;DR

This paper introduces a new thick string-like braneworld model in $f(T)$ gravity, revealing how torsion influences the brane's internal structure, phase transitions, and gravitational spectrum, with implications for bulk geometry and stability.

Contribution

It presents the first $f(T)$ gravity-based thick string-like brane model with torsion-induced internal structures and phase transitions, expanding the understanding of braneworld scenarios in teleparallel gravity.

Findings

Torsion induces internal structure and phase transitions in the brane.

The gravitational spectrum is stable with a localized massless mode.

Torsion modifies the bulk geometry and Planck mass ratio.

Abstract

We propose a codimension two warped braneworld model within the teleparallel $f(T)$ gravity. By assuming a global vortex as the source, we found a $l=0$ vortex solution that yields to a thick string-like brane. Asymptotically, the bulk geometry converges to an $AdS_6$ spacetime whose cosmological constant is produced by the torsion parameters. Furthermore, the torsion induces an $AdS-dS$ transition on the exterior region. Inside the brane core, the torsion produces an internal structure even for a single complex scalar field. As the torsion parameters vary, the brane undergoes a phase transition leading to the formation of ring-like structures. The bulk-brane Planck mass ration is modified by the torsion. The analysis of the stress energy condition reveals a splitting brane process satisfying the weak and strong energy conditions for some values of the parameters. In addition, we investigate the behaviour of the gravitational perturbations in this scenario. It turns out that the gravitational spectrum has a linear behaviour for small masses and is independent of the torsion parameters for large masses. In the bulk, the torsion keeps a gapless non-localizable and stable tower of massive modes. Inside the brane core the torsion produces new barriers and potential wells leading to small amplitude massive modes and a massless mode localized around the ring structures.