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<p>The effective one-body (EOB) theory provides an innovative framework for analyzing the dynamics of binary systems, as articulated by Hamilton’s equations. This paper investigates a self-consistent EOB theory specifically tailored for the dynamics of such systems. Our methodology begins by emphasizing how to effectively utilize the metrics derived from scattering angles in the analysis of binary black hole mergers. We then construct an effective Hamiltonian and formulate a decoupled, variable-separated Teukolsky-like equation for ψ<Stack> <sub>4</sub> <sup><i>B</i></sup> </Stack>. Furthermore, we present the formal solution to this equation, detailing the energy flux, radiation-reaction force (RRF), and waveforms for the “plus” and “cross” modes generated by spinless binaries. Finally, we carry out numerical calculations using the EOB theory and compare the results with numerical relativity (NR) data from the SXS collaboration. The results indicate that to the innermost stable circular orbit, the binding energy—angular momentum relation differs from the NR results by less than 5‰, with a larger mass ratio yielding better agreement.</p>

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Effective one-body theory of spinless binary evolution dynamics

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • Jiliang Jing,
  • Sheng Long,
  • Weike Deng,
  • Jieci Wang

摘要

The effective one-body (EOB) theory provides an innovative framework for analyzing the dynamics of binary systems, as articulated by Hamilton’s equations. This paper investigates a self-consistent EOB theory specifically tailored for the dynamics of such systems. Our methodology begins by emphasizing how to effectively utilize the metrics derived from scattering angles in the analysis of binary black hole mergers. We then construct an effective Hamiltonian and formulate a decoupled, variable-separated Teukolsky-like equation for ψ 4 B . Furthermore, we present the formal solution to this equation, detailing the energy flux, radiation-reaction force (RRF), and waveforms for the “plus” and “cross” modes generated by spinless binaries. Finally, we carry out numerical calculations using the EOB theory and compare the results with numerical relativity (NR) data from the SXS collaboration. The results indicate that to the innermost stable circular orbit, the binding energy—angular momentum relation differs from the NR results by less than 5‰, with a larger mass ratio yielding better agreement.