On the vanishing of Love numbers for Kerr black holes

Abstract

It was shown recently that the static tidal response coefficients, called Love numbers, vanish identically for Kerr black holes in four dimensions. In this work, we confirm this result and extend it to the case of spin-0 and spin-1 perturbations. We compute the static response of Kerr black holes to scalar, electromagnetic, and gravitational fields at all orders in black hole spin. We use the unambiguous and gauge-invariant definition of Love numbers and their spin-0 and spin-1 analogs as Wilson coefficients of the point particle effective field theory. This definition also allows one to clearly distinguish between conservative and dissipative response contributions. We demonstrate that the behavior of Kerr black hole responses to spin-0 and spin-1 fields is very similar to that of the spin-2 perturbations. In particular, static conservative responses vanish identically for spinning black holes. This implies that vanishing Love numbers are a generic property of black holes in four-dimensional general relativity. We also show that the dissipative part of the response does not vanish even for static perturbations due to frame-dragging.

Observation of Gravitational Waves from Two Neutron Star–Black Hole Coalescences

“…The tidal deformability of NSs is imprinted in the GW signal and investigated using the parameter estimation techniques of Section 4. In contrast, BHs have zero tidal deformability (Binnington & Poisson 2009;Damour & Nagar 2009;Chia 2020;Charalambous et al 2021;Le Tiec & Casals 2021). We infer the tidal deformability Λ 2 of the NSs in GW200105 and GW200115 using the NSBH waveform models that include tides.…”

Spin effects in the effective field theory approach to Post-Minkowskian conservative dynamics

“…This transformation (applied to perturbations of the background) may also play a key role in understanding the vanishing of (static) tidal response for rotating black holes[61,[148][149][150] following the pattern observed in Schwarzschild[151][152][153] (http://www.youtube.com/watch?v=v9fvAohXD8g&t=45m15s).…”

Quadratic-in-spin interactions at fifth post-Newtonian order probe new physics

“…It is exactly for this reason that it is crucial to diligently tackle the matching of these Wilson coefficients, as they are bound to uncover further new physics of gravity for black holes, and also of QCD for neutrons stars. Indeed, recently, as the 5PN point-mass interaction has been completed, there has been a surge of independent works that have been studying the rotational Love numbers of black holes and neutron stars associated with C E 2 , C B 2 [46][47][48][49][50][51], which arrived at various new findings and insights. It remains for future theoretical studies and comparison with GW data to also uncover the new physics of gravity and of QCD that is encapsulated in the new Wilson coefficients, C E 2 S 2 and C B 2 S 2 , that we found here.…”