Relativistic and Dynamical Love

TL;DR

This paper develops a comprehensive relativistic model of dynamical tidal interactions in binary neutron stars, improving gravitational wave analysis accuracy by avoiding biases in parameter estimation.

Contribution

It introduces a complete mode expansion for dynamical tides in full general relativity and derives an effective harmonic oscillator equation for mode amplitudes.

Findings

Mode amplitudes satisfy a forced harmonic oscillator equation.

Relativistic treatment improves gravitational-wave parameter estimation.

Provides a complete mode expansion for dynamical tides.

Abstract

Gravitational waves emitted in the late inspiral of binary neutron stars are affected by their tidal deformation. We study the tidal dynamics in full general relativity through matched-asymptotic expansions and prove that the dynamical tidal response can be expanded in a complete set of modes. We further prove that the mode amplitudes satisfy an effective, forced harmonic oscillator equation, which generalizes the overlap-integral formulation of Newtonian gravity. Our relativistic treatment of dynamical tides will avoid systematic biases in future gravitational-wave parameter estimation.