Spinning Black Holes Fall in Love

TL;DR

This paper investigates the tidal deformability of Kerr black holes, proving that nonspinning black holes have vanishing Love tensors while spinning ones exhibit small but nonzero Love tensors, revealing their rigidity.

Contribution

It provides the first analytical computation of Love tensors for spinning black holes, showing their nonzero values at linear order in spin and tidal perturbation.

Findings

Love tensors vanish for nonspinning black holes.

Spinning black holes have small but nonzero Love tensors.

Black holes are highly rigid objects with minimal tidal deformability.

Abstract

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 of compact objects such as astrophysical (Kerr) black holes under an external static tidal field. We prove that all Love tensors 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 tensors are generically nonzero for a spinning black hole. Specifically, to linear order in the Kerr black hole spin and the weak perturbing tidal field, we compute in closed form the Love tensors that couple the mass-type and current-type quadrupole moments to the electric-type and magnetic-type quadrupolar tidal fields. For a dimensionless spin ~ 0.1, the nonvanishing quadrupolar Love tensors are ~ 0.002, thus showing that black holes are particularly "rigid" compact objects.