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 tensorΨ4in the effective spacetime,we utilize the method proposed by Sasaki et al.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 a2and a3in the effective metric.

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 to include binary systems with slowly spinning black holes.Initially,we decompose the equation for the null tetrad component of the gravitationally perturbed Weyl tensorψ_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.