Effective metric of spinless binaries with radiation-reaction effect up to fourth Post-Minkowskian order in effective-one-body theory

TL;DR

This paper derives an effective metric for spinless binary systems including radiation-reaction effects up to the fourth post-Minkowskian order, foundational for the effective-one-body approach in gravitational wave physics.

Contribution

It introduces a self-consistent method to fix parameter freedoms in the effective metric ensuring unified modeling of Hamiltonian, radiation-reaction forces, and waveforms.

Findings

Effective metric constructed up to 4PM order

Parameter freedoms fixed via Weyl tensor component decoupling

Provides foundation for consistent EOB modeling of gravitational waves

Abstract

By means of the scattering angles, we obtain an effective metric of spinless binaries with radiation-reaction effects up to fourth post-Minkowskian order, which is the foundation of the effective-one-body theory. We note that there are freedoms for the parameters of the effective metric because one equation corresponds to two parameters for each post-Minkowskian order. Accordingly, in order to construct a self-consistent effective-one-body theory in which the Hamiltonian, radiation-reaction forces and waveforms for the ``plus" and ``cross" modes of the gravitational wave should be based on the same physical model, we can fix these freedoms by requiring the null tetrad component of the gravitationally perturbed Weyl tensor $\Psi_4^B$ to be decoupled in the effective spacetime.