A Self-Linking Field Formalism

The Gauss-linking integral for disjoint oriented smooth closed curves is derived linking integrals from the Biot-Savart description of the magnetic field. DeTurck and Gluck extend this linking from 3-space R3 to SU (2) space of the unit 3-sphere and hyperbolic space in Minkowski R1,3. I herein extend Gauss-linking to self-linking and develop the concept of self-dual, which is then applied to gravitomagnetic dynamics. My purpose is to redefine Wheeler’s geon from unstable field structures based on the electromagnetic field to self-stabilized gravitomagnetic field structures.