Self-consistent effective-one-body theory for spinless binaries based on post-Minkowskian approximation I:Hamiltonian and decoupled equation forψ^(B)_(4)

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 forψ^(B)_(4)=h_(+)−ih_(×),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 forψ^(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.