Dynamics Of Spin Effects Of Two Black Holes

With development of celestial mechanics and astrophysics, understanding of the universe, gravitational waves detection has become the hot issues for decades. When the gravitational waves reach the ground, it is extremely weak, but it is diffcult to detect.It is to be required a high accuracy theory template. the continuity gravitational waves is a good choice to detect. So, the spinning compact binaries made of neutron stars or black holes,which has become the most ideal sources to detect the gravitational waves.This paper shows that the post-Newtonian amiltonian formulation of the two black holes with the Newtonian part and the pure orbital part up to3PN and the spin-orbit contributions up to3.5PN, in spite of having7independent of exct solating integrals,we have no way to say tha the dynamical is integrable owing to use of the noncanonical spin coordinates. We make the spin variables canonical, system consists of12dimension reduced to10dimension and contains five independent of exct isolating integrals, including the total energy, three components of the total angular momentum vector, and the length of the orbital angular momentum. As the spin-spin effects are further included, only the length of the orbital angular momentum is no longer conserved, so that the dynamics becomes typically non-integrable. Numerical simulations support the onset of chaos. In addition, a threshold value of the maximum ratio of the spin-spin Hamiltonian to the whole Hamiltonian for distinguishing between the ordered and chaotic cases is given.Finally, through numerical simula, we figure the system configuration, cross section diagram and the gravitational waveform. We found that the gravitational wave of the order orbit is ordered and changes periodically,but the gravitational wave of the chaotic orbit is chaotic, and it showes the unpredictability and clutter clear. This work provides the reference to the gravitational waves detection and do enough theoretical preparation...