The open question of whether a black hole can become tidally deformed by an external gravitational field has profound implications for fundamental physics , astrophysics and gravitational-wave astronomy .
Love numbers characterize the tidal deformability of compact objects such as astrophysical ( Kerr ) black holes .
We prove that all Love numbers vanish identically for a Kerr black hole in the nonspinning limit or for an axisymmetric tidal perturbation .
In contrast to this result , we show that Love numbers are generically nonzero for a spinning black hole .
Specifically , to linear order in the black hole spin and the weak perturbing tidal field , we compute in closed form the Love numbers that couple the mass-type and current-type quadrupole moments to the electric-type and magnetic-type quadrupolar tidal fields .
This tidal deformability is potentially observationally important through its contribution to the accumulated gravitational-wave phase of an inspiralling stellar-mass compact object into a massive black hole .
We show that for a dimensionless black hole spin \sim 0.1 , the nonvanishing quadrupolar Love numbers are \sim 2 \times 10 ^ { -3 } .
This indicates that , despite black holes being particularly “ stiff ” compact objects , their nonvanishing tidal deformability could be detected by the future gravitational-wave interferometer LISA .