Effective metric for binaries in framework of EOB theory to fifth PM order

TL;DR

This work develops a self-consistent effective-one-body framework in the post-M Minkowskian regime, targeting 5PM accuracy to meet next-generation gravitational-wave detector needs. By constructing a Petrov type D effective metric and deriving an energy map between real and effective two-body systems, the authors fix PM coefficients up to 5PM through careful matching of real and EOB scattering angles. They provide explicit 5PM expressions for the real and effective scattering angles and determine the a_i coefficients of the effective metric, enabling a rotating, type-D spacetime in which the decoupled equation for the Weyl perturbation component $\psi_4^B$ can be separated. The resulting framework yields a unified description of Hamiltonian dynamics, radiation reaction, and waveforms, with clear pathways for comparison to numerical relativity and extension to rapidly rotating binaries for future detector-era gravitational-wave modeling.

Abstract

To establish a self-consistent effective one-body (EOB) theory that describes the dynamical evolution of binary systems based on the post-Minkowskian (PM) approximation, where the Hamiltonian, radiation reaction force, and waveforms are derived from an effective metric, the primary objective is to obtain the effective metric. Given that third generation gravitational wave detectors require at least fifth-order PM accuracy, in this paper we constructed an effective metric in the EOB theory of binaries up to fifth PM order. The effective metric is of type D, allowing for the derivation of decoupled and variable-separable equations for the null tetrad component of the gravitational perturbed Weyl tensor. This presents a basis for us to establish a self-consistent EOB theory up to 5PM order.