两圈阶及3.5阶后牛顿精度的八极轫致辐射波形
Octupolar bremsstrahlung waveform up to the two-loop level and the third-and-a-half post-Newtonian accuracy
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中文总结 AI 辅助
该研究在MPM形式下计算两质量散射中偶宇称八极引力波形至两圈及3.5PN精度，并通过与EFT结果对比验证了其正确性。
中文摘要 AI 辅助
我们扩展了最近的工作（该工作聚焦于波形的偶宇称四极部分），计算了偶宇称八极贡献 $U_3$，它对应于两质量散射过程中发射的引力波形 $W \equiv \frac{c^4 r}{4G} \bar m^{i} \bar m^{j } h_{i j}$。我们在多极后闵可夫斯基（MPM）形式框架内工作，并使用3.5阶后牛顿（PN）精度的辐射反应准开普勒表示来描述双曲运动。我们显式地评估了 $U_3$ 的频域值 $\hat U_3(\omega, \theta,\phi)$，直至两圈阶，即 $h_{ij}(\omega, \theta,\phi)$ 的 $O(G^4)$ 贡献，对应于 $\hat U_3(\omega, \theta,\phi)$ 的 $O(G^3)$ 贡献。作为我们结果的关键部分确认，我们发现，当精确考虑我们先前四极比较中推导出的两种形式中质心原点定义上的相同（2.5PN阶）差异时，我们3.5PN频域MPM波形的单圈截断与现有的有效场论（EFT）结果一致。
英文摘要
Extending our recent work (which focussed on the even-parity quadrupolar part of the waveform), we compute the even-parity octupolar contribution, $U_3$, to the gravitational waveform $W \equiv \frac{c^4 r}{4G} \bar m^{i} \bar m^{j } h_{i j}$ emitted during the scattering of two masses. We work within the Multipolar Post-Minkowskian (MPM) formalism, and use the 3.5 Post-Newtonian (PN) accurate radiation-reacted quasi-Keplerian representation of the hyperbolic motion. We explicitly evaluate the frequency-domain value $\hat U_3(ω, θ,ϕ)$ of $U_3$ up to the 2-loop level, i.e. $ O(G^4)$ contributions to $h_{ij}(ω, θ,ϕ)$, corresponding to $O(G^3)$ contributions to $\hat U_3(ω, θ,ϕ)$. As a crucial partial confirmation of our result, we find that the 1-loop truncation of our 3.5 PN frequency-domain MPM waveform agrees with corresponding existing Effective Field Theory (EFT) results when taking into account exactly the {\it same} (2.5PN-level) difference in the definitions of the center-of-mass origins within the two formalisms that was deduced from our previous quadrupolar comparison.
发表机构
- Istituto per le Applicazioni del Calcolo “M. Picone” CNR（意大利国家研究委员会计算应用研究所）
- Institut des Hautes Etudes Scientifiques（高等科学研究所）
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