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Scattering of Spinning Black Holes from Exponentiated Soft Factors

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Vines,  Justin
Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Guevara, A., Ochirov, A., & Vines, J. (2019). Scattering of Spinning Black Holes from Exponentiated Soft Factors. Journal of High Energy Physics, 2019(9): 056. doi:10.1007/JHEP09(2019)056.


Cite as: http://hdl.handle.net/21.11116/0000-0002-BB91-7
Abstract
We provide evidence that the classical scattering of two spinning black holes is controlled by the soft expansion of exchanged gravitons. We show how an exponentiation of Cachazo-Strominger soft factors, acting on massive higher-spin amplitudes, can be used to find spin contributions to the aligned-spin scattering angle through one-loop order. The extraction of the classical limit is accomplished via the on-shell leading-singularity method and using massive spinor-helicity variables. The three-point amplitude for arbitrary-spin massive particles minimally coupled to gravity is expressed in an exponential form, and in the infinite-spin limit it matches the stress-energy tensor of the linearized Kerr solution. A four-point gravitational Compton amplitude is obtained from an extrapolated soft theorem, equivalent to gluing two exponential three-point amplitudes, and becomes itself an exponential operator. The construction uses these amplitudes to: 1) recover the known tree-level scattering angle at all orders in spin, 2) match previous computations of the one-loop scattering angle up to quadratic order in spin, 3) lead to new one-loop results through quartic order in spin. These connections map the computation of higher-multipole interactions into the study of deeper orders in the soft expansion.