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

TL;DR

This paper develops an effective metric within the EOB framework for binary systems, achieving fifth-order PM accuracy essential for next-generation gravitational wave detection.

Contribution

It constructs a type D effective metric in EOB theory up to fifth PM order, enabling decoupled equations for gravitational perturbations.

Findings

Effective metric of type D constructed up to 5PM order

Decoupled equations derived for gravitational perturbations

Foundation laid for a self-consistent 5PM EOB theory

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.