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

TL;DR

This paper proposes a simple, practical metamaterial design to emulate Schwarzschild-(anti-)de Sitter spacetime, using homogenized isotropic dielectric and magnetic particles, enabling experimental exploration of gravitational effects.

Contribution

It introduces a straightforward metamaterial formulation based on homogenized isotropic components to realize Tamm mediums for Schwarzschild-(anti-)de Sitter spacetime, avoiding complex nanostructures.

Findings

Demonstrated the ability to access a wide range of parameters via particle shape, volume fraction, and material properties.

The formulation is valid outside the event horizon for Schwarzschild spacetime and inside for de Sitter spacetime.

No restrictions for anti-de Sitter spacetime.

Abstract

While metamaterials offer the potential to realize Tamm mediums which represent vacuous spacetime subjected to gravitational fields, practical formulations for suitable metamaterials have not hitherto been developed. This matter is 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 which lie outside the event horizon for Schwarzschild spacetime and inside the event horizon for de Sitter spacetime; there are no such restrictions for anti-de Sitter spacetime.