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

TL;DR

This paper introduces a new self-consistent effective one-body theory for spinless binaries based on the post-Minkowskian approximation, improving computational efficiency and removing small velocity assumptions.

Contribution

The authors develop a novel effective one-body framework applicable to any post-Minkowskian order, unifying the construction of Hamiltonian, radiation-reaction force, and waveform.

Findings

Decoupled equation for gravitational perturbation in effective metric

Applicable to all post-Minkowskian orders without small velocity assumption

Reduced computational effort for radiation-reaction and waveform calculations

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 $\psi^{B}_{4}$ 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.