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Abstract

The tidal response of a compact object is a key gravitational-wave observable
encoding information about its interior. This link is subtle due to the
nonlinearities of general relativity. We show that considering a scattering
process bypasses challenges with potential ambiguities, as the tidal response
is determined by the asymptotic in- and outgoing waves at null infinity. As an
application of the general method, we analyze scalar waves scattering off a
nonspinning black hole and demonstrate that the frequency-dependent tidal
response calculated for arbitrary dimensions and multipoles reproduces known
results for the Love number and absorption in limiting cases. In addition, we
discuss the definition of the response based on gauge-invariant observables
obtained from an effective action description, and clarify the role of analytic
continuation for robustly (i) extracting the response and the physical
information it contains, and (ii) distinguishing high-order post-Newtonian
corrections from finite-size effects in a binary system. Our work is important
for interpreting upcoming gravitational-wave data for subatomic physics of
ultradense matter in neutron stars, probing black holes and gravity, and
looking for beyond standard model fields.