从振幅到具有立方相互作用和潮汐效应的引力辐射
From amplitudes to gravitational radiation with cubic interactions and tidal effects
摘要：
本文研究了立方和潮汐相互作用对两个非自旋天体合并的螺旋相发射的引力波谱的影响。有两个独立的宇称偶三次相互作用项，我们取之为$I_1 = {R^{αβ}}_{μν} {R^{μν}}_{ρσ} {R^{ρσ}}_{αβ}$和$G_3 = I_1-2 R^α\,_μ\,^β\,_ν R^μ\,_ρ\,^ν\,_σ R^ρ\,_α\,^σ\,_β$。后者具有消失的纯引力子振幅，但修改了混合标量/引力子振幅，这对我们的研究至关重要。在有效场论的框架下，计算了由于$I_1$、$G_3$和潮汐相互作用对四极矩的修正，由此得到了在扰动过程中辐射到一阶的引力波的功率和在后闵可夫斯基展开过程中辐射到一阶的功率.的$I_1$预测是新颖的，我们发现，我们的结果为$G_3$是有关的潮汐扰动所产生的已知的四极校正，虽然物理起源的$G_3$耦合是无关的潮汐相互作用的有限大小的影响。我们通过重新计算潮汐修正和提出一个明确的场重新定义来证明这一点。在后牛顿展开中，我们的结果在首阶是完整的，对于$G_3$和潮汐相互作用，引力波通量为5 PN，对于$I_1$为6PN。最后，我们计算波形的相应修改。
英文摘要：
We study the effect of cubic and tidal interactions on the spectrum of gravitational waves emitted in the inspiral phase of the merger of two non-spinning objects. There are two independent parity-even cubic interaction terms, which we take to be $I_1 = {R^{αβ}}_{μν} {R^{μν}}_{ρσ} {R^{ρσ}}_{αβ}$ and $G_3 = I_1-2 R^α\,_μ\,^β\,_ν R^μ\,_ρ\,^ν\,_σ R^ρ\,_α\,^σ\,_β$. The latter has vanishing pure graviton amplitudes but modifies mixed scalar/graviton amplitudes which are crucial for our study. Working in an effective field theory set-up, we compute the modifications to the quadrupole moment due to $I_1$, $G_3$ and tidal interactions, from which we obtain the power of gravitational waves radiated in the process to first order in the perturbations and leading order in the post-Minkowskian expansion. The $I_1$ predictions are novel, and we find that our results for $G_3$ are related to the known quadrupole corrections arising from tidal perturbations, although the physical origin of the $G_3$ coupling is unrelated to the finite-size effects underlying tidal interactions. We show this by recomputing such tidal corrections and by presenting an explicit field redefinition. In the post-Newtonian expansion our results are complete at leading order, which for the gravitational-wave flux is 5PN for $G_3$ and tidal interactions, and 6PN for $I_1$. Finally, we compute the corresponding modifications to the waveforms.
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