Gravitational metamaterials from optical properties of spacetime media

Abstract: Gravitational optical properties are here investigated under the hypothesis of spherically-symmetric spacetimes behaving as media. To do so, we first consider two different definitions of the refractive index, $n_O$, of a spacetime medium and show how to pass from one definition to another by means of a coordinate transformation. Accordingly, the corresponding physical role of $n_O$ is discussed by virtue of the Misner-Sharp mass and the redshift definition. Afterwards, we discuss the inclusion of the electromagnetic fields and the equivalence with nonlinear effects induced by geometry. Accordingly, the infrared and ultraviolet gravity regimes are thus discussed, obtaining bounds from the Solar System, neutron stars and white dwarfs, respectively. To do so, we also investigate the Snell's law and propose how to possibly distinguish regular solutions from black holes. As a consequence of our recipe, we speculate on the existence of \emph{gravitational metamaterials}, whose refractive index may be negative and explore the corresponding physical implications, remarking that $n_O<0$ may lead to invisible optical properties, as light is bent in the opposite direction compared to what occurs in ordinary cases. Further, we conjecture that gravitational metamaterials exhibit a particle-like behavior, contributing to dark matter and propose three toy models, highlighting possible advantages and limitations of their use. Finally, we suggest that such particle-like configurations can be ``dressed" by interaction, giving rise to \emph{geometric quasiparticles}. We thus construct modifications of the quantum propagator as due to nonminimal couplings between curvature and external matter-like fields, finding the corresponding effective mass through a boson mixing mechanism.