Gravitational waves in the Hyperspace?

In the framework of the debate on high-frequency gravitational waves (GWs), after a review of GWs in standard General Relativity, which is due for completness, the possibility of merging such a traditional analysis with the Hyperspace formalism that has been recently introduced in some papers in the literature, with the goal of a better understanding of manifolds dimensionality also in a cosmological framework, is discussed. Using the concept of refractive index in the Hyperspace, spherical solutions are given and the propagation of GWs in a region of the Hyperspace with an unitary refractive index is also discussed. Propagation phenomena associated to the higher dimensionality are proposed, possibly including non-linear effects. Further and accurate studies in this direction are needed.