Spinning Black Hole Scattering at $\mathcal{O}(G^3 S^2)$: Casimir Terms, Radial Action and Hidden Symmetry
University of Edinburgh（爱丁堡大学）；Florida State University（佛罗里达州立大学）；Universidad Nacional Autónoma de México（墨西哥国立自治大学）；University of California at Los Angeles（加州大学洛杉矶分校）
Dogan Akpinar, Fernando Febres Cordero, Manfred Kraus, Michael S. Ruf, Mao Zeng
备注：
45 pages, 3 figures. v2: journal published version + additional typo corrections. v3: additional typo corrections
我们从固定有限自旋的有质量散射振幅出发，解决了双体系统后闵可夫斯基动力学在自旋展开计算中的微妙问题。具体而言，表观上模糊的自旋卡西米尔项可通过不同自旋表示的有质量振幅之间的插值，利用振幅自旋对角部分关于$S^2 = -s(s+1)\boldsymbol{\text{ħ}}^2$的梯度完全确定。我们从最小耦合引力的自旋0与自旋1粒子的双圈振幅中，提取了自旋0与自旋黑洞在$\boldsymbol{\text{O}}(G^3 S^2)$阶保守散射角中的自旋卡西米尔项，发现其与文献中的已知结果一致。这完善了此前一项研究[Phys. Rev. Lett. 130 (2023), 021601]，该研究从振幅中计算了非卡西米尔项。我们还利用电动力学中的自旋体模型说明我们的方法，发现散射振幅预测与根克尔（root-Kerr）电磁背景下的经典预测在$\boldsymbol{\text{O}}(\boldsymbol{\text{α}}^3 S^2)$阶内一致。对于引力和电动力学，振幅的有限部分在自旋对齐极限下与双体径向作用量重合，将振幅-作用量关系推广到自旋非零的情况。令人惊讶的是，双圈振幅在探针极限下表现出隐藏的自旋移位对称性，该对称性此前在单圈时已被观测到。我们推测该对称性在耦合常数的所有阶都成立，是探针极限下克尔轨道在自旋的前几阶可积性的结果。
英文摘要：
We resolve subtleties in calculating the post-Minkowskian dynamics of binary systems, as a spin expansion, from massive scattering amplitudes of fixed finite spin. In particular, the apparently ambiguous spin Casimir terms can be fully determined from the gradient of the spin-diagonal part of the amplitudes with respect to $S^2 = -s(s+1)\hbar^2$, using an interpolation between massive amplitudes with different spin representations. From two-loop amplitudes of spin-0 and spin-1 particles minimally coupled to gravity, we extract the spin Casimir terms in the conservative scattering angle between a spinless and a spinning black hole at $\mathcal{O}(G^3 S^2)$, finding agreement with known results in the literature. This completes an earlier study [Phys. Rev. Lett. 130 (2023), 021601] that calculated the non-Casimir terms from amplitudes. We also illustrate our methods using a model of spinning bodies in electrodynamics, finding agreement between scattering amplitude predictions and classical predictions in a root-Kerr electromagnetic background up to $\mathcal{O}(α^3 S^2)$. For both gravity and electrodynamics, the finite part of the amplitude coincides with the two-body radial action in the aligned spin limit, generalizing the amplitude-action relation beyond the spinless case. Surprisingly, the two-loop amplitude displays a hidden spin-shift symmetry in the probe limit, which was previously observed at one loop. We conjecture that the symmetry holds to all orders in the coupling constant and is a consequence of integrability of Kerr orbits in the probe limit at the first few orders in spin.
The recently established formalism of a worldline quantum field theory, which describes the classical scattering of massive bodies in Einstein gravity, is generalized up to quadratic order in spin -- for a pair of Kerr black holes revealing a hidden ${\mathcal N}=2$ supersymmetry. The far-field time-domain waveform of the gravitational waves produced in such a spinning encounter is computed at leading order in the post-Minkowskian (weak field, but generic velocity) expansion, and exhibits this supersymmetry. From the waveform we extract the leading-order total radiated angular momentum in a ge…
Comments on the hidden symmetries of the spinning point particle in Kerr-Newman, D = 5 minimal gauged supergravity and higher dimensional spacetimes with Killing-Yano torsion
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Hidden simplicity in AdS spinning Mellin amplitudes via scaffolding
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study & ICTP-AP（杭州高等研究院基础物理与数学学院及ICTP-亚太中心）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Peng Huanwu Center for Fundamental Theory（彭桓武理论物理中心）
The Kerr/CFT correspondence provides a holographic description of spinning black holes that exist in our universe, and the notion of hidden conformal symmetry allows for a formulation of this correspondence away from extremality. In this work we study how hidden conformal symmetry is manifest when we consider dynamics beyond the Klein-Gordon equation, through studying the analytic structure of higher derivative equations of motion of a massless probe scalar field on a Kerr background using the monodromy method. Since such higher derivative dynamics appear in known examples of holographic AdS/l…
Hidden simplicity in the scattering for neutron stars and black holes
Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh（爱丁堡大学物理与天文学学院希格斯理论物理中心）；Theoretical Physics Department, CERN（欧洲核子研究中心理论物理部）
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