Energy flux and waveforms by coalescing spinless binary system in effective one-body theory

We present a study on the energy radiation rate and waveforms of the gravitational wave generated by coalescing spinless binary systems up to the third post-Minkowskian approximation in the effective one-body theory. To derive an analytical expansion of the null tetrad components of the gravitational perturbed Weyl tensor ${\Psi }_4$ in the effective spacetime, we utilize the method proposed by Sasaki $et$ $al\mathrm{.}$ During this investigation, we discover more general integral formulas that provide a theoretical framework for computing the results in any order. Subsequently, we successfully compute the energy radiation rate and waveforms of the gravitational wave, which include the results of the Schwarzschild case and the correction terms resulting from the dimensionless parameters $a_2$ and $a_3$ in the effective metric.