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We advocate for the existence of an alternative description of the scattering and gravitational radiation phenomena of black holes based on complex angular momentum techniques (analytic continuation of partial wave expansions, S-matrix duality, and effective resummations involving Regge poles and associated residues, Regge trajectories, semiclassical interpretations, etc.). These techniques, which have proven to be very useful in various areas of physics (i.e., in quantum mechanics, in electromagnetism and optics, in acoustics and seismology, and in high energy physics) for describing and analyzing resonant scattering, have only been marginally employed in the context of black hole physics.