Towards a realization of Schwarzschild-(anti-)de Sitter spacetime as a particulate metamaterial

While metamaterials offer the potential to realize Tamm mediums that are electromagnetically equivalent to vacuous spacetime subjected to gravitational fields, practical formulations for suitable metamaterials have not hitherto been developed. This matter was addressed by establishing a metamaterial formulation for the Tamm medium representing Schwarzschild-(anti-)de Sitter spacetime. Our formulation is remarkably simple and does not involve a complex nanostructure of the type that is often associated with metamaterials. Instead it is based on the homogenization of only isotropic dielectric and isotropic magnetic component mediums, which are distributed randomly as oriented spheroidal particles. Using the inverse Bruggeman homogenization formalism, we demonstrated that a wide range of constitutive parameter values for the Tamm medium may be accessed through varying the particle shape, volume fraction, or relative permittivity and relative permeability of the component mediums. The presented formulation is appropriate for the regions of spacetime that lie outside the event horizon for Schwarzschild spacetime and inside the cosmological horizon for de Sitter spacetime; there are no such restrictions for anti-de Sitter spacetime.