  The gravitational polarizability properties of black holes are compared and
contrasted with their electromagnetic polarizability properties. The "shape" or
"height" multipolar Love numbers h_l of a black hole are defined and computed.
They are then compared to their electromagnetic analogs h_l^{EM}. The Love
numbers h_l give the height of the l-th multipolar "tidal bulge" raised on the
horizon of a black hole by faraway masses. We also discuss the shape of the
tidal bulge raised by a test mass m, in the limit where m gets very close to
the horizon.
