Abstract
We compute the classical tree-level five-point amplitude for the two-to-two scattering of spinning celestial objects with the emission of a graviton. Using this five-point amplitude, we then turn to the computation of the leading-order time-domain gravitational waveform. The method we describe is suitable for arbitrary values of classical spin of Kerr black holes and does not require any expansion in powers of the spin. In this paper we illustrate it in the simpler case of the scattering of one Kerr and one Schwarzschild black hole. An important ingredient of our calculation is a novel form of the Compton amplitude with spinning particles including contact terms derived from matching to black-hole perturbation theory calculations. This ensures that our waveform is valid up to at least fourth order in the spin. Our method can be applied immediately to generate improved waveforms once higher-order contact terms in the Compton amplitude become available. Finally, we show the formula for the gravitational memory to all orders in the spin, which is in agreement with our results.
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Acknowledgments
We would like to thank Massimo Bianchi, Emil Bjerrum-Bohr, Stefano De Angelis, Thibault Damour, Claudio Gambino, Paolo Pichini, Fabio Riccioni and Marcos Skowronek for several interesting conversations. GT thanks the Physics Department at the University of Rome “Tor Vergata” for their warm hospitality and support. This work was supported by the Science and Technology Facilities Council (STFC) Consolidated Grants ST/P000754/1 “String theory, gauge theory & duality” and ST/T000686/1 “Amplitudes, strings & duality”. The work of GRB and JG is supported by an STFC quota studentship. GC has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 847523 “INTERACTIONS”. No new data were generated or analysed during this study.
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Brandhuber, A., Brown, G.R., Chen, G. et al. Resummed spinning waveforms from five-point amplitudes. J. High Energ. Phys. 2024, 26 (2024). https://doi.org/10.1007/JHEP02(2024)026
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DOI: https://doi.org/10.1007/JHEP02(2024)026