Abstract
We continue to investigate correspondences between, on the one hand, scattering amplitudes for massive higher-spin particles and gravitons in appropriate quantum-to-classical limits, and on the other hand, classical gravitational interactions of spinning black holes according to general relativity. We first construct an ansatz for a gravitational Compton amplitude, at tree level, constrained only by locality, crossing symmetry, unitarity and consistency with the linearized-Kerr 3-point amplitude, to all orders in the black hole’s spin. We then explore the extent to which a unique classical Compton amplitude can be identified by comparing with the results of the classical process of scattering long-wavelength gravitational waves off an exact Kerr black hole, determined by appropriate solutions of the Teukolsky equation. Up to fourth order in spin, we find complete agreement with a previously conjectured exponential form of the tree-level Compton amplitude. At higher orders, we extract tree-level contributions from the Teukolsky amplitude by an analytic continuation from a physical (a/GM < 1) to a particle-like (a/GM > 1) regime. Up to the sixth order in spin, we identify a unique conservative part of the amplitude which is insensitive both to the choice of boundary conditions at the black hole horizon and to branch choices in the analytic continuation. The remainder of the amplitude is determined modulo an overall sign from a branch choice, with the sign flipping under exchanging purely ingoing and purely outgoing boundary conditions at the horizon. Along the way, we make contact with novel applications of massive spinor-helicity variables pertaining to their relation to EFT operators and (spinning) partial amplitudes.
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Acknowledgments
We thank Francesco Alessio, Stefano de Angelis, Zvi Bern, Lucille Cangemi, Marco Chiodaroli, Gustav Jakobsen, Henrik Johansson, Dimitris Kosmopoulos, David Kosower, Andrés Luna, Gustav Mogull, Julio Parra-Martinez, Alexander Ochirov, Donal O’Connell, Jan Plefka, Radu Roiban, M. V. S. Saketh, Matteo Sergola, Chia-Hsien Shen, Nils Siemonsen, Jan Steinhoff, Fei Teng, and Mao Zeng for useful discussions. We are grateful to Rafael Aoude, Kays Haddad and Andreas Helset for agreeing to exchange preliminary drafts of our works, including [20]. A.G. and J.V. are grateful for hospitality at KITP Santa Barbara, during the program ‘High-Precision Gravitational Waves’. A.G. is supported by a Junior Fellowship at the Harvard Society of Fellows, as well as by the DOE grant de-sc/0007870. The work of Y.F.B. has been supported in part by the European Research Council under Advanced Investigator Grant ERC-AdG-885414. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Research, Innovation and Science. This publication has emanated from research supported in part by a Grant from Science Foundation Ireland under Grant number 21/PATH-S/9610.
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Bautista, Y.F., Guevara, A., Kavanagh, C. et al. Scattering in black hole backgrounds and higher-spin amplitudes. Part II. J. High Energ. Phys. 2023, 211 (2023). https://doi.org/10.1007/JHEP05(2023)211
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DOI: https://doi.org/10.1007/JHEP05(2023)211