Effective action and linear response of compact objects in Newtonian gravity

TL;DR

This paper adapts an effective field theory approach from general relativity to Newtonian gravity, modeling compact stars with multipole moments and analyzing their oscillation modes and tidal resonances.

Contribution

It introduces a formalism representing compact objects by multipole moments with response functions, linking oscillation modes to tidal interactions in Newtonian gravity.

Findings

Response functions encode star oscillation modes.

Resonances occur between modes and tidal forces.

Framework can be extended to general relativity.

Abstract

We apply an effective field theory method for the gravitational interaction of compact stars, developed within the context of general relativity, to Newtonian gravity. In this effective theory a compact object is represented by a point particle possessing generic gravitational multipole moments. The time evolution of the multipoles depends on excitations due to external fields. This can formally be described by a response function of the multipoles to applied fields. The poles of this response correspond to the normal oscillation modes of the star. This gives rise to resonances between modes and tidal forces in binary systems. The connection to the standard formalism for tidal interactions and resonances in Newtonian gravity is worked out. Our approach can be applied to more complicated situations. In particular, a generalization to general relativity is possible.