Gravitomagnetic Coupling in a Weak Field Approximation

According to general relativity, a moving or rotating matter should produce contribution to the gravitational field which is in analogy to the magnetic field of a moving charge or magnetic dipole; we can thus express the general relativity in a Maxwellian structure with the existence of single operator for both fields. In this research work, we studied the coupling of Maxwell's dynamical theory of electromagnetism in a non-static gravitational field by applying an obtained gravitational scalar potential to the Riemann's laplacian operator. In the limit of weak gravitation, we obtained the dynamical gravitomagnetic scalar potential across the fields. While in the boundary conditions the results are generalized gravitomagnetic potential. our results will thus widen the scope into study of gravitomagnetic coupling.