Tidal Love Numbers of Kerr Black Holes

Understand

The open question of whether a Kerr black hole can become tidally deformed or not has profound implications for fundamental physics and gravitational-wave astronomy.

• We consider a Kerr black hole embedded in a weak and slowly varying, but otherwise arbitrary, multipolar tidal environment.
• By solving the static Teukolsky equation for the gauge-invariant Weyl scalar $\psi_0$, and by reconstructing the corresponding metric perturbation in an ingoing radiation gauge, for a general harmonic index $\ell$, we compute the linear response of a Kerr black hole to the tidal field.
• This linear response vanishes identically for a Schwarzschild black hole and for an axisymmetric perturbation of a spinning black hole.