Dynamical tidal response of Kerr black holes from scattering amplitudes

We match scattering amplitudes in point particle effective field theory (EFT) and general relativity to extract low frequency dynamical tidal responses of rotating (Kerr) black holes to all orders in spin. In the conservative sector, we study local worldline couplings that correspond to the time -derivative expansion of the black hole tidal response function. These are dynamical (frequency -dependent) generalizations of the static Love numbers. We identify and extract couplings of three types of subleading local worldline operators: the curvature time derivative terms, the spin -curvature time derivative couplings, and quadrupole-octupole mixing operators that arise due to the violation of spherical symmetry. The first two subleading couplings are nonzero and exhibit a classical renormalization group running; we explicitly present their scheme -independent beta functions. The conservative mixing terms, however, vanish as a consequence of vanishing static Love numbers. In the nonconservative sector, we match the dissipation numbers at next -to -leading and next -to -next -to leading orders in frequency. In passing, we identify terms in the general relativity absorption probabilities that originate from tails and short -scale logarithmic corrections to the lowest order dissipation contributions.