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

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.