Vanishing of black hole tidal Love numbers from scattering amplitudes

TL;DR

This paper demonstrates that Kerr black holes have zero static tidal Love numbers by analyzing scattering amplitudes, confirming their vanishing and providing gauge-invariant results that clarify the origin of tidal effects.

Contribution

The authors derive the vanishing of Kerr black hole Love numbers directly from scattering amplitudes, offering a gauge-invariant and coordinate-independent proof that clarifies the tidal response origin.

Findings

Kerr black holes have zero static Love numbers for all perturbations.

Tidal effects originate solely from the black hole potential region.

The approach confirms known scalar Love number behavior in higher dimensions.

Abstract

We extract the black hole (BH) static tidal deformability coefficients (Love numbers) and their spin-0 and spin-1 analogs by comparing on-shell amplitudes for fields to scatter off a spinning BH in the worldline effective field theory (EFT) and in general relativity (GR). We point out that the GR amplitudes due to tidal effects originate entirely from the BH potential region. Thus, they can be separated from gravitational non-linearities in the wave region, whose proper treatment requires higher order EFT loop calculations. In particular, the elastic scattering in the near field approximation is produced exclusively by tidal effects. We find this contribution to vanish identically, which implies that the static Love numbers of Kerr BHs are zero for all types of perturbations. We also reproduce the known behavior of scalar Love numbers for higher dimensional BHs. Our results are manifestly gauge-invariant and coordinate-independent, thereby providing a valuable consistency check for the commonly used off-shell methods.