  Revisiting Einstein's gravitational theory, we build a five-dimensional
braneworld. Within this framework, one announces the appearance of symmetric
and asymmetric domain walls. Furthermore, it examines the emergent
four-dimensional gravity from a theory with non-canonical dynamics. Exploring
the physical and mathematical aspects, e.g., brane's energy density and the
Kaluza-Klein (KK) spectrum, one verifies that brane splitting is absent in the
canonical and non-canonical theories. Additionally, we note the localization of
the four-dimensional fluctuation projection on the 3-branes, which ensures the
theory's stability. Thereby, one can conclude that the behavior of
gravitational perturbations of the domain wall maintains a profile similar to a
stable and non-localizable tower of massive modes. In contrast, within the
brane core, the matter sector generates new barriers and potential wells,
resulting in massive modes with approximately symmetric amplitudes. However,
the non-canonical dynamics generate massive modes with asymmetric amplitudes
far from the 3-brane.
