Inspiral to Ring-down, an Almost Exact One-Body Approach

XOB provides an almost eXact One-Body approach for the conservative part of binary merger dynamics of general relativity, which applies to the full three stages of the merger process, and allows the feature of gravitational waves be related to the inner-structure of merging bodies directly. We clarify the sense of exactness of this approach in this work and calculate the gravitational waveform of black hole binary merger process subsequently. Our calculation shows that, the waveform exhibits damping tail only when the BHs possess regular internals and experience rotational symmetry enhancement as the merger progresses on. Basing on this point, we calculate lower and upper boundings for the real part of the lowest tone quasi-normal frequency of the merger product and get results consistent with observations.