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Working within the post-Minkowskian approach to General Relativity, we prove that the radiation-reaction to the emission of gravitational waves during the large-impact-parameter scattering of two (classical) point masses modifies the conservative scattering angle by an additional contribution of order $G^3$ which involves a high-energy (or massless) logarithmic divergence of opposite sign to the one contained in the third-post-Minkowskian result of Bern et al.
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T. Damour, “Gravitational radiation and the motion of compact bodies”, in Deruelle, N. and Piran, T., eds., Gravitational Radiation
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