On the gravitational polarizability of black holes
Abstract
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 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.
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