Vanishing Love Numbers of Kerr-Newman Black Holes

Tidal Love numbers characterize the conservative response of compact objects to external perturbations and provide a powerful probe of their nature. While the static Love numbers of Schwarzschild, Kerr, and Reissner–Nordström black holes remarkably vanish, the tidal response of a generic Kerr–Newman black hole has remained unexplored due to the intrinsic coupling between gravitational and electromagnetic perturbations. Exploiting a recent breakthrough in the separability of these perturbations, we analytically determine the static tidal response of the most general stationary black hole in four-dimensional Einstein–Maxwell theory. For arbitrary multipole order, charge, and spin, we show that the entire matrix of conservative Love numbers vanishes, including the mixed gravito-electromagnetic couplings. We also compute the nonvanishing static dissipative response induced by frame dragging.