实现Schwarzschild-（反）de Sitter时空作为一种微粒超材料
Towards a realization of Schwarzschild-(anti-)de Sitter spacetime as a particulate metamaterial
摘要：
虽然超材料提供了实现Tamm介质的可能性，Tamm介质代表了受到引力场的真空时空，但迄今为止还没有开发出合适的超材料的实用配方。这个问题是通过建立一个超材料制定的塔姆介质代表史瓦西-（反）德西特时空。我们的公式非常简单，不涉及通常与超材料相关的复杂纳米结构类型。相反，它是基于均匀化的只有各向同性的电介质和各向同性的磁成分介质，随机分布的定向球状颗粒。使用逆Bruggeman均匀化形式主义，我们证明了广泛的本构参数值的Tamm介质可以通过改变颗粒的形状，体积分数或相对介电常数和相对磁导率的组成介质。所提出的公式适用于史瓦西时空位于事件视界之外，德西特时空位于事件视界之内的时空区域;反德西特时空则没有这样的限制。
英文摘要：
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.
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