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 ${\psi }_4^B$ 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.