A class of 5D inhomogeneous models with a cosmological constant

In this work we would like to address the problem of the effect of bulk matter on the brane cosmological evolution in a general way. We assume that the spatial part of the brane metric is not maximally symmetric, therefore spatially inhomogeneous. However we retain the conformal flatness property of the standard cosmological model (FRW) i.e. the Weyl tensor of the induced 4D geometry is zero. We refer to it as Spatially Inhomogeneous
Irrotational (SII) brane. It is shown that the model can be regarded as the 5D generalization of the SII spacetimes found recently (Pantelis S. Apostolopoulos, Phys. Rev. D 94 (2016) no.12, 124052 [arXiv:1612.01853 [gr-qc]).