Dynamics And Gravitional Waves For The System Of Halos And Kerr Black Hole With Pesudo-Newtonian Potential

If general theory of relativity can be regarded as the exact theory to describe the interaction gravity between objects, Newton’s theory of gravitation shoud be the approximate description at low speed in macro world. Currently, Newton’s theory of gravitation is applied generally to calculate motion law of the celestial bodies. Space Science and Technology of many countries mainly adopts the celestial mechanics methods based on Newton’s theory of gravitation, which is already mature. Although the correction from general relativity to precessionofperihelion of mercury is in less than one percent of the resault from celestial mechanics which is on the basis of Newtonian mechanics, the Newton’s theory of gravitation can’t describe exactly gravitational field around the black hole with high density. The equations of general relativity of general balck hole are very difficult to acquire. Even if the results can be obtained in certain instances, the forms of which are always too complicated.The pseudo-Newtonian potentials which are acquired by adding small correction on the Newtonian potential have very simple mathematical forms with some essential relativistic effects and have the same convenience to the Newtional potential when is applied to construct a superposed gravitational field.The regular and chaotic dynamics of the test particle in a superposed field between a pseudo-Newtonian Kerr black hole and quadrupolar halos is studied detailedly in this article. In particular, the dynamical dependence on each of the two parameters including the quadrupolar parameter of the halos and the spin angular momentum of the rotating black hole is focused on. As a result, the small quadrupolar moment except the spin angular momentum does not have a great effect on the stability and radii of the innermost stable circular orbits of these test particles. In addition, chaos does mainly occur for small absolute values of the rotating parameters, and does not at all exist for the maximum counter-rotating case or the maximum co-rotating one under some sets of initial conditions and other parameters. This means that the rotating parameters of the black hole weaken the chaotic properties. It is also found that the counter-rotating system is more unstable than the co-rotating system. On the other hand, chaos is not at all present for small absolute values of the quadrupoles, but the onset of chaos is easier for the prolate halos than for the oblate ones. A close relation between gravitational waveforms and the types of trajectories in a superposed field between a pseudo-Newtonian Kerr black hole and quadrupolar halos is shown in detail. The gravitational waveforms emitted from circular, KAM tori and chaotic orbits must be periodic, quasiperiodic and stochastic, respectively. The chaotic motion can maximally enhance both the amplitudes and the energy emission rates of the waves.