Why should a kinetic amplitude factor for Monopole charge be considered in non-static space-time in the case of Bogomolny Equation

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. The monopole charge’s kinetic factor is deduced by classical field theory and quantum field conception respectively.