On Interaction of Scalar Field and Gravitational Field in condition of Bogomolny Equation Concurrently on gauge charge kinetic factor of monopole in curved spacetime

By a resolution for classical Yang-Mills-Higgs functional results in the static metric curved space, with the Bogomolny equation for scalar field in flat space, deduce the interaction form between scalar field and gravitational field, furthermore, applying Higgs mechanism on Higgs particle interact with a gauge gravity field then work out the same terms of this interaction result. Note that in spacetime equipped with non-static metric there is no existing closed isochronous hypersurface which is isomorphism to sphere in 3D space, normally in this condition the Bogomolny equation for magnetic monopoles’ research is not easy to operate. But for the inner product of field curvature in the condition of Bogomolny equation, it is feasible to do an analysis that by the Hodge Dual on volume 3-form on space domain and 1-form on time domain in 4D Riemannian manifold, hence calculate the difference between the motional monopole charge in static metric compared with that in non-static metric. Meanwhile, in scope of quantum field, the evolution operator of monopole is also demonstrated to develop the magnetic monopole’s kinetic effects in curved spacetime. To some extent, the kinetic factor for monopoles has the similar hint of covariant derivative with the scalar field particles.