Metamaterials are synthetic materials that exhibit properties not usually found in natural materials. One such property that has beenof great importance to the study of optics is a negative refractive index within the metamaterial. This property implies negative permeabilityand permittivity for the metamaterial. Using and deriving the electro-magnetic stress energy tensor in Minkowski space as an approximationin the weak field limit, the gravitational curvature effects of such meta-materials will be investigated. The basic example of a capacitor andinductor will be used to illustrate the mathematical results.