Self-consistent Effective-one-body theory for spinless binaries based on post-Minkowskian approximation I: Hamiltonian and decoupled equation for $\psi^B_{4}$

TL;DR

This paper develops a self-consistent effective-one-body (EOB) model for spinless binaries using post-Minkowskian approximation, deriving a decoupled equation for gravitational wave perturbations to unify the Hamiltonian, radiation-reaction force, and waveform.

Contribution

It introduces a novel effective spacetime and decoupled wave equation within the EOB framework based on post-Minkowskian approximation for spinless binaries.

Findings

Derived a decoupled equation for $oldsymbol{ ext{psi}^B_4}$ using the effective spacetime.

Established a self-consistent EOB model for spinless binaries.

Unified the Hamiltonian, waveform, and radiation-reaction force in the EOB framework.

Abstract

To build a self-consistent effective-one-body (EOB) theory, in which the Hamiltonian, radiation-reaction force and waveform for the "plus" and "cross" modes of the gravitational wave should be based on the same effective background spacetime, the key step is to look for the decoupled equation for $\psi^B_{4}=\ddot{h}_{+}-i\ddot{h}_{\times}$, which seems a very difficult task because there are non-vanishing tetrad components of the tracefree Ricci tensor for such spacetime. Fortunately, based on an effective spacetime obtained in this paper by using the post-Minkowskian (PM) approximation, we find the decoupled equation for $\psi^B_{4}$ by dividing the perturbation part of the metric into the odd and even parities. With the effective metric and decoupled equation at hand, we set up a frame of self-consistent EOB model for spinless binaries.