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Self-consistent effective-one-body theory for spinless binaries based on post-Minkowskian approximation I: Hamiltonian and decoupled equation for \(\psi _4^{\rm{B}}\)

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Abstract

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 for \(\psi _4^{\rm{B}} = {\ddot h_ +} - {\rm{i}}{\ddot h_ \times}\), 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 for \(\psi _4^{\rm{B}}\) 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.

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Authors and Affiliations

  1. Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, 410081, China

    Jiliang Jing, Shuai Chen, Manman Sun, Mengjie Wang & Jieci Wang

  2. Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, Yangzhou, 225009, China

    Jiliang Jing

  3. School of Mathematics and Statistics, Hunan First Normal University, Changsha, 410205, China

    Xiaokai He

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  1. Jiliang Jing
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  2. Shuai Chen
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Correspondence to Jiliang Jing or Jieci Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12035005, 12122504, and 11875025), and National Key Research and Development Program of China (Grant No. 2020YFC2201400). We would like to thank professors S. Chen and Q. Pan for useful discussions on the manuscript.

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Jing, J., Chen, S., Sun, M. et al. Self-consistent effective-one-body theory for spinless binaries based on post-Minkowskian approximation I: Hamiltonian and decoupled equation for \(\psi _4^{\rm{B}}\). Sci. China Phys. Mech. Astron. 65, 260411 (2022). https://doi.org/10.1007/s11433-022-1885-6

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