{"title":"无自旋二元演化动力学的有效一体理论","authors":"Jiliang Jing, Sheng Long, Weike Deng, Jieci Wang","doi":"10.1007/s11433-025-2758-5","DOIUrl":null,"url":null,"abstract":"<div><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<span>\n <sup><i>B</i></sup><sub>4</sub>\n \n </span>. 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></div>","PeriodicalId":774,"journal":{"name":"Science China Physics, Mechanics & Astronomy","volume":"68 12","pages":""},"PeriodicalIF":7.5000,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Effective one-body theory of spinless binary evolution dynamics\",\"authors\":\"Jiliang Jing, Sheng Long, Weike Deng, Jieci Wang\",\"doi\":\"10.1007/s11433-025-2758-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><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<span>\\n <sup><i>B</i></sup><sub>4</sub>\\n \\n </span>. 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></div>\",\"PeriodicalId\":774,\"journal\":{\"name\":\"Science China Physics, Mechanics & Astronomy\",\"volume\":\"68 12\",\"pages\":\"\"},\"PeriodicalIF\":7.5000,\"publicationDate\":\"2025-09-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Science China Physics, Mechanics & Astronomy\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11433-025-2758-5\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Science China Physics, Mechanics & Astronomy","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11433-025-2758-5","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Effective one-body theory of spinless binary evolution dynamics
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 ψB4. 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.
期刊介绍:
Science China Physics, Mechanics & Astronomy, an academic journal cosponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China, and published by Science China Press, is committed to publishing high-quality, original results in both basic and applied research.
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