  We present an analytic method for calculating the tidal response function of
a nonrotating and a slowly rotating black hole from the Teukolsky equation in
the small-frequency and near horizon limit. We point out that in the
relativistic context, there can be two possible definitions of the tidal Love
numbers and the dissipative part that arises from the tidal response function.
Our results suggest that both of these definitions predict zero tidal Love
numbers for a nonrotating black hole. On the other hand, for a slowly rotating
black hole in a generic tidal environment, these two definitions of the tidal
Love numbers do not coincide. While one procedure suggests zero tidal Love
numbers, the other procedure gives purely imaginary tidal Love numbers. As
expected, the dissipative terms differ as well. We emphasize that in our
analysis, we keep all the terms linear in the frequency, unlike previous works
in the literature. Following this, we propose a procedure to calculate the
tidal response function -- and hence the Love numbers -- for an arbitrarily
rotating black hole.
