Gravitomagnetic Dipole Moment of Gravitational Unit Cells

It is proposed that gravitational meta-atom unit cells with gravitomagnetic moments could exhibit gravitomagnetic permeability, analogous to the magnetic permeability of materials comprised of atoms with magnetic moments. Recently, a gravitoelectromagnetic (GEM) framework was proposed to explore the possibility of a Veselago-inspired approach to gravitational metamaterials. The prospect of gravitational metamaterials motivates the consideration of candidate gravitational unit cells or gravitational meta-atoms. Although mass serves as a monopole source of a gravitoelectric field similar to positive charge, negative mass would be needed to create a gravitational analog of an electric dipole. However, moving mass is analogous to electric current, and can lead to a gravitomagnetic dipole moment analogous to magnetic dipole moments of magnetic materials and atoms. In this paper, GEM field approximations to general relativity are used to find the gravitomagnetic dipole moment of different rotating systems, ranging in scale from meters to astronomical size.