Regular Article – Theoretical Physics
Energy map and effective metric in an effective-one-body theory based on the second-post-Minkowskian approximation
Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, 410081, Changsha, Hunan, People’s Republic of China
2 School of Mathematics and Computational Science, Hunan First Normal University, 410205, Changsha, People’s Republic of China
3 Department of Astronomy, Beijing Normal University, 100875, Beijing, People’s Republic of China
Accepted: 24 January 2021
Published online: 30 January 2021
Effective-one-body (EOB) theory was originally proposed based on the post-Newtonian (PN) approximation and plays an important role in the analysis of gravitational wave signals. Recently, the post-Minkowskian (PM) approximation has been applied to the EOB theory. The energy map and the effective metric are the two key building blocks of the EOB theory, and in PN approximation radial action variable correspondence is employed to construct the energy map and the effective metric. In this paper, we employ the PM approximation up to the second order, and use the radial action variable correspondence and the precession angle correspondence to construct the energy map and the effective metric. We find that our results based on the radial action variable correspondence, are exactly the same with those obtained based on the precession angle correspondence. Furthermore, we compare the results obtained in this work to the previous existing ones.
© The Author(s) 2021
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