String-like brane splitting in the context of \(f(T,\mathcal {B})\) gravity

In this work, the influence of the boundary term \(\mathcal {B}\) is analyzed in a string-like thick brane scenario in the gravity context \(f(T,\mathcal {B})\). For that, three models of \(f(T,\mathcal {B})\) are proposed, i. e., \(f_1(T,\mathcal {B})=T+k\mathcal {B}^{n}\), \(f_2(T,\mathcal {B})=T+k(-T+\mathcal { B})^{n}\) and \(f_3(T,\mathcal {B})=T+k_1T^2+k_2\mathcal {B}^2\), where n, k and \(k_{1,2}\) are parameters that control the deviation from the usual teleparallelism. The first relevant result obtained was the appearance of a super-located tower in the core for energy density. Furthermore, the greater the influence of the boundary term, the new maximums and minimums appear in the energy density. All this indicates the emergence of capable structures from split to the brane. The second relevant result was obtained by analyzing the gravitational perturbations, where the effective potential presents the supersymmetric form of quantum mechanics, leading to well-localized massless modes.