Tidal Effects in the Post-Minkowskian Expansion

TL;DR

This paper extends scattering amplitude and effective field theory methods to include tidal effects in neutron star mergers, providing new finite size corrections to the conservative dynamics at higher post-Minkowskian orders.

Contribution

It introduces the first computation of next-to-leading order tidal corrections to the post-Minkowskian Hamiltonian for neutron star mergers.

Findings

Derived gauge-invariant expressions for tidal corrections.

Confirmed consistency with test-body and existing post-Newtonian results.

Provided scattering amplitudes and angles for tidal effects.

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.