The thick brane scenario built on the f (T, B) teleparallel gravity theory was considered for the study of phase transitions, internal structures and new classes of solutions in a model. In this theory, T denotes the torsion scalar, and B is a boundary term. An interesting result was observed when brane splitting occurs, i. e., internal structures in the model arise as a consequence of the appearance of new domain walls in the theory. In fact, this preliminary result influences the profile of the matter field (from kink to multi-kink) so that for appropriate values of the parameters k 1,2 multiple phase transitions are identified. To perform this analysis, the Differential Configurational Entropy (DCE) that has the ability to predict the existence of phase transitions through critical points was used. Furthermore, the DCE is able to select the most stable solutions since it gives us details about the informational content to the field settings.

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.

We study a spin 1/2 fermion in a thick braneworld in the context of teleparallel f(T, B) gravity. Here, f(T, B) is such that $$f_1(T,B)=T+k_1B^{n_1}$$ f 1 ( T , B ) = T + k 1 B n 1 and $$f_2(T,B)=B+k_2T^{n_2}$$ f 2 ( T , B ) = B + k 2 T n 2 , where $$n_{1,2}$$ n 1 , 2 and $$k_{1,2}$$ k 1 , 2 are parameters that control the influence of torsion and the boundary term. We assume Yukawa coupling, where one scalar field is coupled to a Dirac spinor field. We show how the $$n_{1,2}$$ n 1 , 2 and $$k_{1,2}$$ k 1 , 2 parameters control the width of the massless Kaluza–Klein mode, the breadth of non-normalized massive fermionic modes and the properties of the analogue quantum-potential near the origin.

The thick brane scenario built on the [Formula: see text] teleparallel gravity theory was considered for the study of phase transitions, internal structures and new classes of solutions in a model. In this theory, [Formula: see text] denotes the torsion scalar and [Formula: see text] is a boundary term. An interesting result was observed when brane splitting occurs, i.e. internal structures in the model arise as a consequence of the appearance of new domain walls in the theory. In fact, this preliminary result influences the profile of the matter field (from kink to multikink) so that for appropriate values of the parameters [Formula: see text], multiple phase transitions are identified. To perform this analysis, the Differential Configurational Entropy (DCE) that has the ability to predict the existence of phase transitions through critical points was used. Furthermore, the DCE is able to select the most stable solutions since it gives us details about the informational content to the field settings.

Braneworld models are interesting theoretical and phenomenological frameworks to search for new physics beyond the standard model of particles and cosmology. In this work, we discuss braneworld models whose gravitational dynamics is governed by teleparallel [Formula: see text] gravities. Here, we emphasize a codimension two-axisymmetric model, also known as a string-like brane. Likewise, in the 5D domain-wall models, the [Formula: see text] gravitational modification leads to a phase transition on the perfect fluid source providing a brane-splitting mechanism. Furthermore, the torsion changes the gravitational perturbations. The torsion produces new potential wells inside the brane core leading to a massless mode more localized around the ring structures. In addition, the torsion keeps a gapless nonlocalizable and a stable tower of massive modes in the bulk.