Gravitational Radiation Of Gravitational Magnetic Monopoles And Low-speed Gravitational Dual Charge Particle

In order to make the Maxwell's equations with source more symmetric, Dirac put forward the idea of magnetic poles and gave out the formula of the quantization ofelectricity in quantum mechanics. Then he clearly stated that, each pole should be corresponding to an end of half-infinity string of singularity (i.e. Dirac string), so-called Dirac monopole theory. This theory can help people to express Maxwell's equations in the dual form.In this paper, by introducing doublet four-dimensional vector potentials, the electromagnetic radiation of the low and high speed moving dyons are discussed respectively. Likewise, first, in the weak field approximation, we find that Einstein's equations unveil a Maxwell-type structure by comparison of gravitation with electromagnetism. Based on the similarity between Einstein's equations and the Maxwell's equations, there should exist the gravitomagnetic monopole (the gravitomagnetic charge) to compare with the mass (the gravitoelectric charge), and the symmetrized form of linearized Einstein's equations is obtained naturally. In addition, the method of small parameter is used to calculate the multipolar expansion of gravitational radiation in classical situation by analogy with electromagnetism.Second, based on the duality relation between gravitoelectric and gravitomagnetic charges, the generalized gravitational field equations in the presence of the two charges are derived via the variational principle. It is important that, in the weak field approximation, these equations can open up a familiar structure being analogous to the form of Dirac-Maxwell's equations. Such the situation not only shows the similarity between the gravitational field and the electromagnetic field, but also illustrates the obtained results are reasonable. In addition, the gravitational radiation for low speed moving Gravitational Dyons is given out, and we discuss the property further if the mass and the dual mass exits in space only.