引力三次有效场论中的自旋波形
Spinning waveforms in cubic effective field theories of gravity
AI总结：
本文推导了两个克尔黑洞在引力三次有效场论形变下散射的最低阶时域波形的全自旋阶解析表达式，采用三种独立方法，并发现部分形变可通过 Newman-Janis 型平移联系标量波形，同时证明引力记忆无最低阶修正。
摘要：
我们推导了两个任意质量与自旋矢量的克尔黑洞在爱因斯坦-希尔伯特引力的所有独立三次形变存在时散射所产生的最低阶时域波形的全自旋阶解析表达式。这些形变包括两个宇称偶相互作用 $I_1$ 和 $G_3$，以及宇称奇相互作用 $\ ilde{I}_1$ 和 $\ ilde{G}_3$。我们的结果通过三种独立方法获得：一种特别高效的直接积分与张量约化方法；分部积分结合微分方程方法；以及留数计算。对于 $G_3$ 和 $\ ilde{G}_3$ 形变，我们可以用适当平移碰撞参数后的标量波形来表示自旋波形，这让人联想到 Newman-Janis 平移。对于 $I_1$ 和 $\ ilde{I}_1$，也存在类似的平移，但还伴随有额外的贡献，这些贡献不能简单地通过对标量 $I_1$ 和 $\ ilde{I}_1$ 波形进行平移来捕捉。我们还证明了引力记忆不存在最低阶修正。我们的解析结果非常紧凑，并比较了获得这些结果所用三种方法的有效性。我们还简要评论了三次形变对可观测量修正的大小。
英文摘要：
We derive analytic all-order-in-spin expressions for the leading-order time-domain waveforms generated in the scattering of two Kerr black holes with arbitrary masses and spin vectors in the presence of all independent cubic deformations of Einstein-Hilbert gravity. These are the two parity-even interactions $I_1$ and $G_3$, and the parity-odd ones $\tilde{I}_1$ and $\tilde{G}_3$. Our results are obtained using three independent methods: a particularly efficient direct integration and tensor reduction approach; integration by parts combined with the method of differential equations; and finally a residue computation. For the case of the $G_3$ and $\tilde{G}_3$ deformations we can express the spinning waveform in terms of the scalar waveform with appropriately shifted impact parameters, which are reminiscent of Newman-Janis shifts. For $I_1$ and $\tilde{I}_1$ similar shifts occur, but are accompanied by additional contributions that cannot be captured by simply shifting the scalar $I_1$ and $\tilde{I}_1$ waveforms. We also show the absence of leading-order corrections to gravitational memory. Our analytic results are notably compact, and we compare the effectiveness of the three methods used to obtain them. We also briefly comment on the magnitude of the corrections to observables due to cubic deformations.
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