Tidal deformation and dissipation of rotating black holes

We show that rotating black holes do not experience any tidal deformation when they are perturbed by a weak and adiabatic gravitational field. The deformability of an object is quantified the so-called ``Love numbers,'' which describe object's linear response to its external In this work, we compute Love numbers Kerr find vanish identically. also dissipative part hole's response, nonvanishing due absorptive nature event horizon. Our results hold for arbitrary values hole spin, both electric-type magnetic-type perturbations, all orders in multipole expansion boundary conditions at horizon asymptotic infinity incorporated our study, as crucial understanding way these effects mapped onto gravitational-wave observables. closing, address ambiguity issue general relativity, argue resolved those taken into account. findings provide essential inputs current efforts probe compact objects through waves emitted binary systems.