On the gravitational polarizability of black holes

TL;DR

This paper investigates the gravitational polarizability of black holes by defining and computing their Love numbers, comparing them with electromagnetic analogs, and analyzing the shape of tidal bulges near the horizon.

Contribution

It introduces the concept of gravitational Love numbers for black holes, computes them, and compares these with electromagnetic counterparts, providing new insights into black hole tidal responses.

Findings

Black holes have specific gravitational Love numbers h_l.

Comparison shows differences between gravitational and electromagnetic polarizability.

Analysis of tidal bulge shape near the horizon enhances understanding of black hole responses.

Abstract

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.