Compact Non-Linear Gravitomagnetic Fields as Dark Matter

We introduce a model of dark matter inspired by non-linear gravito-electromagnetism formulation of Roy Maartens and Bruce Bassett. The model is a fully covariant 1 + 3 electromagnetic analogy of gravity characterized by Weyl gravito-electric and gravito-magnetic spatial tensor fields in which the Bianchi identities are the dynamical equations. The nonlinear rotationally invariant vacuum Bianchi equations describe the properties of space-time within a given locality. We identify the compact gravito-magneto field as a Ricci soliton in Einstein’s field equations that describes 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.