Thick string-like braneworlds in f(T) gravity

Abstract

We propose a codimension two warped braneworld model within the teleparallel [Formula: see text] gravity. Asymptotically, the bulk geometry converges to an [Formula: see text] spacetime whose cosmological constant is produced by the torsion parameters. Furthermore, the torsion induces an AdS-dS transition on the exterior region. As the torsion parameters vary, the brane undergoes a phase transition from a thick string-like brane into 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 behavior of the gravitational perturbations in this scenario. It turns out that the gravitational spectrum has a linear behavior for small masses and is independent of the torsion parameters for large masses. In the bulk, the torsion keeps a gapless nonlocalizable 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.

Teleparallel gravity: Effects of torsion in 6D braneworlds

“…That feature reflects the brane internal structure, which shows a splitting and forms a ring-like structure. A similar result was obtained considering a power-law modified gravity for which f (T ) = T + kT n , where k and n are two torsion parameters controlling the departure of the usual teleparallel theory [38]. Here, a noteworthy feature is the violation of the dominant energy condition for f 1 and f 2 .…”

“…We now investigate the effects of torsion on the propagation of the gravitational perturbations. Consider the seschsbein perturbation [38]…”

“…and a 4D plane-wave satisfying ( − m 2 ) µν = 0. So, the perturbed Einstein equation (31) leads to [38] 4A…”

“…In the equation above, we can see that the torsion adds a new term proportional to f T T /f T when compared to the GR based string-like braneworld [38,40,41].…”

“…An interesting consequence is the brane splitting, since the torsion modifies the source equation of state and the dynamics of the gravitational perturbations. Some of the present authors, studied a f (T ) gravity model in a codimension-two braneworld scenario, also known as the string-like branes [38]. This kind of teleparallel gravity model has axially symmetric solutions of the GR equations, which provide some interesting physical results [11,[39][40][41][42].…”