  Intrinsic Conformal Symmetries have emerged as a tool for developing viable
and physically coherent models, particularly in scenarios incorporating a
negative cosmological constant. This study demonstrates that when the bulk
geometry accommodates a set of $10$ Intrinsic Conformal Symmetries, which
operate on three-dimensional hypersurfaces (be they spacelike or timelike), it
leads to the existence of two distinct families of five-dimensional spacetimes.
These spacetimes represent the general solutions to the bulk field equations.
An aspect of these models is the composition of their energy-momentum tensor,
which includes two key components: a negative cosmological constant and a
parallel pressure $p_{\parallel}$ aligned with the extra spatial dimension.
This framework can be perceived as a $5D$ extension of the recently identified
Spatially Inhomogeneous and Irrotational spacetimes. Significantly, these
models offer a novel perspective for investigating the impacts of spatial
inhomogeneity on the cosmological evolution of the Universe, particularly
within the context of the Randall-Sundrum theory. This exploration is essential
for deepening our understanding of the role of higher dimensions in
cosmological models.
