Response of a Kerr black hole to a generic tidal perturbation

TL;DR

This paper investigates the tidal response of Kerr black holes, finding that static and axisymmetric Love numbers vanish, with non-zero values only arising in non-axisymmetric dynamical cases, and showing how these are affected by spin and perturbation type.

Contribution

It provides a comprehensive analysis of tidal Love numbers for Kerr black holes, including extremal cases, revealing their vanishing in most scenarios and dependence on perturbation characteristics.

Findings

Static and axisymmetric Love numbers vanish for Kerr black holes.

Non-zero Love numbers occur only in non-axisymmetric dynamical perturbations.

Dynamical Love numbers are affected by the sign of the black hole's spin.

Abstract

We derive the response, the real part of which provides the tidal Love numbers, for non-extremal as well as extremal Kerr black holes under generic tidal perturbations. Our results suggest that the static as well as dynamical (linear-in-frequency) Love numbers vanish for both Schwarzschild and slowly rotating (linear-in-angular momentum) Kerr black holes, under generic perturbations. The vanishing of static and dynamical Love numbers also holds for axisymmetric tidal perturbations of non-extremal and extremal Kerr black holes. In fact, even under generic tidal perturbations, the static Love numbers of Kerr black holes vanish identically. The only case with non-zero Love numbers corresponds to the non-axisymmetric dynamical tidal perturbations of Kerr black holes (to arbitrary order of angular momentum). We also demonstrate that the non-zero dynamical Love numbers, for both non-extremal and extremal Kerr black holes, get modified under the change of the sign of the spin-weight, for electromagnetic and gravitational tidal perturbations.