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The effective one-body theories, introduced by Buonanno and Damour, are novelapproaches to constructing a gravitational waveform template. By taking a gaugein which $\psi_{1}^{B}$ and $\psi_{3}^{B}$ vanish, we find a decoupled equationwith separable variables for $\psi^{B}_{4}$ for gravitational perturbation inthe effective metric obtained in the post-Minkowskian approximation.Furthermore, we set up a new self-consistent effective one-body theory forspinless binaries, which can be applicable to any post-Minkowskian orders. Thistheory not only releases the assumption that $v/c$ should be a small quantitybut also resolves the contradiction that the Hamiltonian, radiation-reactionforce, and waveform are constructed from different physical models in theeffective one-body theory with the post-Newtonian approximation. Compared withour previous theory (Science China, 65, 260411, (2022)), the computationaleffort for the radiation-reaction force and waveform in this new theory will betremendously reduced.

New self-consistent effective one-body theory for spinless binaries based on the post-Minkowskian approximation