Energy flux and waveform of gravitational wave generated by coalescing slow-spinning binary system in effective one-body theory

We extend our research on the energy flux and waveform characteristics of gravitational waves generated by merging nonspinning binary black holes through self-consistent effective one-body theory \cite{L2023} to include binary systems with slowly spinning black holes. Initially, we decompose the equation for the null tetrad component of the gravitationally perturbed Weyl tensor \(\psi^B_{4}\) into radial and angular parts, leveraging the second-order approximation of the rotation parameter \(a\). Subsequently, we derive an analytical solution for the radial equation and observe that our results are contingent upon the parameters \(a_2\), \(a_3\) and \(a\), which represent the second- and third-order correction parameters, respectively. Ultimately, we calculate the energy flux, the radiation-reaction force and the waveform for the ``plus" and ``cross" modes of the gravitational waves generated by merging slowly spinning binary black holes.