Tidal Effects in the Post-Minkowskian Expansion

TL;DR

The leading and, for the first time, next-to-leading order post-Minkowskian finite size corrections to the conservative Hamiltonian, together with their associated scattering amplitudes and scattering angles are computed.

Abstract

Tools from scattering amplitudes and effective field theory have recently been repurposed to derive state-of-the-art results for the black hole binary inspiral in the post-Minkowskian expansion. In the present work we extend this approach to include the tidal effects of mass and current quadrupoles on the conservative dynamics of non-spinning neutron star mergers. We compute the leading and, for the first time, next-to-leading order post-Minkowskian finite size corrections to the conservative Hamiltonian, together with their associated scattering amplitudes and scattering angles. Our expressions are gauge invariant and, in the extreme mass ratio limit, consistent with the dynamics of a tidally deformed test body in a Schwarzschild background. Furthermore, they agree completely with existing results at leading post-Minkowskian and second post-Newtonian orders.

Figures (1)

• Figure 1: Feynman diagrams for classical tidal corrections. The thick and thin lines denote massive scalars and exchanged gravitons, respectively, while black circles are tidal operator insertions. Not shown are "reflected" graphs obtained by swapping the scalars, nor "twisted" graphs obtained by swapping the incoming and outgoing legs for one of the scalars.