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arXiv 2402.12342gr-qchep-th
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后闵可夫斯基理论结合自旋有效单体方法处理两体散射问题

Post-Minkowskian Theory Meets the Spinning Effective-One-Body Approach for Two-Body Scattering

Alessandra Buonanno, Gustav Uhre Jakobsen, Gustav Mogull

AI总结:

本文推导了首个包含最高至三圈阶后闵可夫斯基结果的自旋有效单体哈密顿量(SEOB-PM模型),该模型考虑了完整的双曲运动和时间非局域尾效应,与数值相对论数据高度吻合,并可用于生成准圆轨道自旋黑洞的波形模型。

摘要:

LIGO-Virgo-KAGRA合作组织使用的有效单体(EOB)波形,主要是通过对相对论两体问题的后牛顿展开进行重求和而发展起来的。鉴于近期在后闵可夫斯基(PM)理论和引力自力形式方面取得的重大进展,人们对于构建以创新方式整合来自各种微扰方法信息的波形模型产生了浓厚兴趣。在应对未来十年内预期运行的下一代地基探测器(如Einstein Telescope和Cosmic Explorer)以及天基探测器(如LISA、TianQin或Taiji)所带来的精度挑战时,这一点尤为关键。在此背景下,我们推导了首个包含最高至三圈阶PM结果的自旋EOB哈密顿量:SEOB-PM模型。该模型考虑了完整的双曲运动,包括时间非局域尾效应。为了评估其准确性,我们将其对保守散射角的预测(并附加了耗散贡献)与非自旋和自旋等质量黑洞的数值相对论数据进行了比较。我们观察到非常好的一致性,其表现与最近提出的$w_{\ m EOB}$势模型相当,在某些情况下甚至略优于该模型;而SEOB-PM模型正是围绕试探质量极限对该势模型的一种重求和。事实上,在试探质量极限下,SEOB-PM哈密顿量和散射角会退化为Kerr时空中测试粒子的对应结果。一旦补充了束缚轨道的时间非局域贡献,SEOB-PM哈密顿量即可用于生成准圆轨道上自旋黑洞的波形模型。

英文摘要:

Effective-one-body (EOB) waveforms employed by the LIGO-Virgo-KAGRA Collaboration have primarily been developed by resumming the post-Newtonian expansion of the relativistic two-body problem. Given the recent significant advancements in post-Minkowskian (PM) theory and gravitational self-force formalism, there is considerable interest in creating waveform models that integrate information from various perturbative methods in innovative ways. This becomes particularly crucial when tackling the accuracy challenge posed by upcoming ground-based detectors (such as the Einstein Telescope and Cosmic Explorer) and space-based detectors (such as LISA, TianQin or Taiji) expected to operate in the next decade. In this context, we present the derivation of the first spinning EOB Hamiltonian that incorporates PM results up to three-loop order: the SEOB-PM model. The model accounts for the complete hyperbolic motion, encompassing nonlocal-in-time tails. To evaluate its accuracy, we compare its predictions for the conservative scattering angle, augmented with dissipative contributions, against numerical-relativity data of non-spinning and spinning equal-mass black holes. We observe very good agreement, comparable, and in some cases slightly better to the recently proposed $w_{\rm EOB}$-potential model, of which the SEOB-PM model is a resummation around the probe limit. Indeed, in the probe limit, the SEOB-PM Hamiltonian and scattering angles reduce to the one of a test mass in Kerr spacetime. Once complemented with nonlocal-in-time contributions for bound orbits, the SEOB-PM Hamiltonian can be utilized to generate waveform models for spinning black holes on quasi-circular orbits.

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