Spinning Black Hole Scattering at $\mathcal{O}(G^3 S^2)$: Casimir Terms, Radial Action and Hidden Symmetry
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2024
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| author | Akpinar, Dogan Cordero, Fernando Febres Kraus, Manfred Ruf, Michael S. Zeng, Mao |
| author_facet | Akpinar, Dogan Cordero, Fernando Febres Kraus, Manfred Ruf, Michael S. Zeng, Mao |
| contents | We resolve subtleties in calculating the post-Minksowskian 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_19005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spinning Black Hole Scattering at $\mathcal{O}(G^3 S^2)$: Casimir Terms, Radial Action and Hidden Symmetry Akpinar, Dogan Cordero, Fernando Febres Kraus, Manfred Ruf, Michael S. Zeng, Mao High Energy Physics - Theory General Relativity and Quantum Cosmology We resolve subtleties in calculating the post-Minksowskian 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. |
| title | Spinning Black Hole Scattering at $\mathcal{O}(G^3 S^2)$: Casimir Terms, Radial Action and Hidden Symmetry |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2407.19005 |