Scattering of tidally interacting bodies in post-Minkowskian gravity

TL;DR

This work extends the post-Minkowskian framework to tidal interactions in binary systems by coupling finite-size effects to worldlines via an effective field theory with tidal tensors and Love-number-like coefficients. It derives the first-order tidal contributions to the scattering data by evaluating the perturbed on-shell action along unperturbed motion, and translates these results into the EOB formalism as an energy-dependent $Q_{tidal}$ term. The paper provides explicit expressions for integrated tidal invariants and their impact on the scattering angle and periastron precession, including detailed quadrupolar-electric contributions and their high-energy and Newtonian limits. These results offer a bridge between PM gravity, tidal hydrodynamics of neutron stars, and PN/EOB descriptions, with potential applications to waveform modeling and gravitational scattering in strong-field regimes.

Abstract

The post-Minkowskian approach to gravitationally interacting binary systems ({\it i.e.}, perturbation theory in $G$, without assuming small velocities) is extended to the computation of the dynamical effects induced by the tidal deformations of two extended bodies, such as neutron stars. Our derivation applies general properties of perturbed actions to the effective field theory description of tidally interacting bodies. We compute several tidal invariants (notably the integrated quadrupolar and octupolar actions) at the first post-Minkowskian order. The corresponding contributions to the scattering angle are derived.

Figures (1)

• Figure 1: The figure shows the choice of the the axes (adapted to $u_1^\mu$, and to the vectorial impact parameter $b^\mu$), and the origin (located on ${\mathcal{L}}_2$), of the coordinates we use in the text. The $z$ coordinate of any point is assumed to be 0 and is omitted.