The gravitational polarizability properties of black holes are compared and contrasted with their electromagnetic polarizability properties. The ``shape'' or ``height'' multipolar Love numbers hₗ of a black hole are defined and computed. They are then compared to their electromagnetic analogs hₗEM. The Love numbers hₗ give the height of the lth 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.
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Damour et al. (2009) studied this question.
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