Spinning Black Holes Fall in Love

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 tensors characterize the tidal deformability compact objects such as astrophysical (Kerr) holes under static field. We prove that all vanish identically Kerr in nonspinning limit or axisymmetric perturbation. In contrast to this result, we show are generically nonzero spinning hole. Specifically, linear order spin weak perturbing field, compute closed form couple mass-type current-type quadrupole moments electric-type magnetic-type quadrupolar fields. For dimensionless ?0.1, nonvanishing ?2×10?3, thus showing particularly “rigid” objects.Received 2 July 2020Revised 18 September 2020Accepted 16 February 2021DOI:https://doi.org/10.1103/PhysRevLett.126.131102© 2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasClassical holesGravitational wave sourcesTechniquesPerturbation theoryGravitation, Cosmology & Astrophysics