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 <em>R...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 <em>R</em><sup>3</sup> to <em>SU</em> (2) space of the unit 3-sphere and hyperbolic space in Minkowski <em>R</em><sup>1,3</sup>. 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 <em>geon</em> from unstable field structures based on the electromagnetic field to self-stabilized gravitomagnetic field structures.展开更多
文摘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 <em>R</em><sup>3</sup> to <em>SU</em> (2) space of the unit 3-sphere and hyperbolic space in Minkowski <em>R</em><sup>1,3</sup>. 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 <em>geon</em> from unstable field structures based on the electromagnetic field to self-stabilized gravitomagnetic field structures.