Self-consistent effective-one-body theory for spinning binaries based on post-Minkowskian approximation

摘要

This study extends the research on the self-consistent effective-one-body theory of a real spinless two-body system based on the post-Minkowskian approximation(Sci.China-Phys.Mech.Astron.65,100411(2022))to the case of a binary system for the spinning black holes.An effective rotating metric and an improved Hamiltonian for the spinning black hole binaries are constructed.The decoupled equation for the null tetrad component of the gravitational perturbed Weyl tensorψ4B in the effective rotating spacetime is found with the help of the gauge transform characteristics of the Weyl tensors.The decoupled equation is then separated between radial and angular variables in the slowly rotating background spacetime,and a formal solution of ψ_(4)^(B) is obtained.On this basis,the formal expressions of the radiation reaction force and the waveform for the“plus”and“cross”modes of the gravitational wave are presented.These results,obtained in the same effective spacetime,constitute a self-consistent effective-one-body theory for the spinning black hole binaries based on the post-Minkowskian approximation.