Gravitational and Electromagnetic Radiations from Binary Black Holes with Electric and Magnetic Charges: I. Circular Orbits on a Poincar\'{e} Cone.

We derive the effective one-body motion of the dyonic binary and explore features of the static orbit including the chaotic behavior. By using the post-Newtonian method, we calculate the total emission rate of energy and angular momentum due to gravitational radiation and electromagnetic radiation for circular orbits on a Poincare Cone. Moreover, we get the evolution of the orbit and calculate the merger time of the dyonic binary. We find the electric and magnetic charges could significantly suppress the merger time of the dyonic binary. The results of this paper provide rich information on the dyonic binary and can be used to test black holes with magnetic charges.