Gravitational Raman Scattering: a Systematic Toolkit for Tidal Effects in General Relativity

TL;DR

This paper develops a systematic framework using scattering amplitudes and effective field theory to compute tidal effects and Love numbers of compact objects in general relativity, clarifying previous ambiguities and extending to higher dimensions.

Contribution

It introduces a coordinate- and gauge-invariant method for calculating tidal Love numbers and dynamical effects using on-shell scattering amplitudes, including recoil effects and higher-dimensional extensions.

Findings

Leading static Love numbers vanish for black holes.

Dynamical Love numbers are non-zero and logarithmically run.

Love numbers in higher dimensions exhibit renormalization group running.

Abstract

We present a framework for systematic computations of scattering amplitudes for gravitational Raman scattering, -- the inelastic scattering of massless fields off compact relativistic objects. We focus on the small-frequency (post-Minkowskian, PM) regime relevant for the study of tidal effects, which can be mapped onto gravitational wave observables during the inspiraling phase of a merger. We demonstrate that this setup is ideal for systematic studies of tidal effects, in a way that is free from coordinate, gauge, and field redefinition ambiguities. We use a combination of worldline effective field theory, the background field method, and advanced scattering amplitude techniques to derive phase shifts for scattering of spin-$0,1,2$ fields off generic compact objects at third PM order. We demonstrate that the inclusion of the recoil of the object is crucial for consistency of this calculation. Focusing on a particular case of black holes, we extract the leading static and dynamical Love numbers of the spin-0 field and the static Love number of the spin-1 field in four dimensions by matching our EFT amplitudes and calculations in General Relativity. We show, fully on-shell, that the leading static Love numbers vanish identically, while the dynamical Love numbers are not zero and run logarithmically. The latter resolves the ambiguities of previous off-shell matching calculations. We also extend our results to seven dimensions, where spin-2 Love numbers undergo a renormalization group running at 2PM, which we compute explicitly. In addition, we extract the leading static Love numbers of spin-0 and spin-1 fields in five dimensions, which also run.