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

TL;DR

This work develops a gauge- and coordinate-invariant, on-shell framework for gravitational Raman scattering to probe tidal effects in general relativity. By uniting worldline EFT with Schwinger-Keldysh open EFT and modern scattering amplitudes, it computes elastic scattering amplitudes for spin-0, spin-1, and spin-2 fields off compact objects up to 3PM and matches them to BH perturbation theory to extract Love numbers. The key findings include the vanishing of leading static Love numbers for spin-0 and spin-1 on-shell, the nonzero dynamical Love numbers with logarithmic running, and the RG running of Love numbers in higher dimensions (notably 5D and 7D). The framework delivers a universal toolkit for systematically studying tidal effects and has direct implications for interpreting gravitational-wave observations and future high-PM extensions.

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.

Figures (1)

• Figure 1: Depiction of the matching of scattering of gravitational waves from a black hole (LHS), and from point particle (RHS). The black hole picture is adapted from observations by the EHT collaboration EventHorizonTelescope:2019dse.