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arxiv 2509.06448 v1 pith:5NX4VOMM submitted 2025-09-08 gr-qc hep-th

Effective one-body theory of spinless binary evolution dynamics

classification gr-qc hep-th
keywords theorybinarydynamicseffectiveresultsenergyequationnumerical
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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 $\psi^B_4$. 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 $5$\textperthousand, with a larger mass ratio yielding better agreement.

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