  It was shown recently that the static tidal response coefficients, called
Love numbers, vanish identically for Kerr black holes in four dimensions. In
this work, we confirm this result and extend it to the case of spin-0 and
spin-1 perturbations. We compute the static response of Kerr black holes to
scalar, electromagnetic, and gravitational fields at all orders in black hole
spin. We use the unambiguous and gauge-invariant definition of Love numbers and
their spin-0 and spin-1 analogs as Wilson coefficients of the point particle
effective field theory. This definition also allows one to clearly distinguish
between conservative and dissipative response contributions. We demonstrate
that the behavior of Kerr black holes responses to spin-0 and spin-1 fields is
very similar to that of the spin-2 perturbations. In particular, static
conservative responses vanish identically for spinning black holes. This
implies that vanishing Love numbers are a generic property of black holes in
four-dimensional general relativity. We also show that the dissipative part of
the response does not vanish even for static perturbations due to
frame-dragging.
