Compact Non-Linear Gravito-Magnetic Fields as Dark Matter

We introduce a model of dark matter inspired by the non-linear gravito-electromagnetism formalisim of Roy Maartens and Bruce Bessett. The Maartens and Besssett model is a fully covariant 1+3 electromagnetic analogue of gravity characterized by Weyl gravito-elctric and gravito-magnetic spatial tensor fields in which the Bianchi identities are the dynamical equations. The nonlinear rotationally invariant invariant vacuum Bianchi equations describe the properties of spacetime within a given locality. We identify compact gravito-magnetic fields based on this model as a Ricci soliton which when included into General Relativity describe dark matter. This component provides the extra gravity which is currently attributed to a variety of theorized forms of non-baryonic matter collectively known as dark matter.