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We compute the next-to-leading order term in the scattering waveform of uncharged black holes in classical general relativity and of half-BPS black holes in $\mathcal{N}=8$ supergravity.
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T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions , Nucl. Phys. B 580
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S. Caron-Huot and Z. Zahraee, Integrability of Black Hole Orbits in Maximal Supergravity , JHEP 07
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