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The tidal response of a compact object is a key gravitational-wave observableencoding information about its interior. This link is subtle due to thenonlinearities of general relativity. We show that considering a scatteringprocess bypasses challenges with potential ambiguities, as the tidal responseis determined by the asymptotic in- and outgoing waves at null infinity. As anapplication of the general method, we analyze scalar waves scattering off anonspinning black hole and demonstrate that the low-frequency expansion of thetidal response reproduces known results for the Love number and absorption. Inaddition, we discuss the definition of the response based on gauge-invariantobservables obtained from an effective action description, and clarify the roleof analytic continuation for robustly (i) extracting the response and thephysical information it contains, and (ii) distinguishing high-orderpost-Newtonian corrections from finite-size effects in a binary system. Ourwork is important for interpreting upcoming gravitational-wave data forsubatomic physics of ultradense matter in neutron stars, probing black holesand gravity, and looking for beyond-standard-model fields.

Tidal response from scattering and the role of analytic continuation