Gravitational polarizability of black holes

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 $h_l^{\mathrm{EM}}$. 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.

Figure 1

The shape of a meridian section of the tidal bulge raised by a test-mass $m$ located at the north pole of the horizon of a BH.