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

Abstract

The effective one-body theories, introduced by Buonanno and Damour, are novel approaches to constructing a gravitational waveform template. By taking a gauge in which ${\psi }_1^B$ and ${\psi }_3^B$ vanish, we find a decoupled equation with separable variables for ${\psi }_4^B$ for gravitational perturbation in the effective metric obtained in the post-Minkowskian approximation. Furthermore, we set up a new self-consistent effective one-body theory for spinless binaries, which can be applicable to any post-Minkowskian orders. This theory not only releases the assumption that $v/c$ should be a small quantity but also resolves the contradiction that the Hamiltonian, radiation-reaction force, and waveform are constructed from different physical models in the effective one-body theory with the post-Newtonian approximation. Compared with our previous theory (Science China, 65, 260411, (2022)), the computational effort for the radiation-reaction force and waveform in this new theory will be tremendously reduced.

17 pages

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