Multipole moments as a tool to infer from gravitational waves the geometry around an axisymmetric body

TL;DR

This paper explores how gravitational wave observations from binary systems can be used to infer the spacetime geometry of an axisymmetric body by analyzing its multipole moments, building on previous theoretical frameworks.

Contribution

It demonstrates a method to extract the central body's multipole moments from gravitational wave data, advancing the understanding of spacetime geometry inference.

Findings

Multipole moments can encode the spacetime structure around axisymmetric bodies.

A procedure to extract multipole moments from gravitational wave signals is outlined.

The approach builds on and extends previous theoretical models.

Abstract

A binary system, composed of a compact object orbiting around a massive central body, will emit gravitational waves which will depend on the central body's spacetime geometry. We expect that the gravitational wave observables will somehow ``encode'' the information about the spacetime structure. On the other hand, it has been known for some time that the geometry around an axisymmetric body can be described by its (Geroch-Hansen) multipole moments. Therefore one can speculate that using the multipole moments can prove to be a helpful tool for extracting this information. We will try to demonstrate this in this talk, following the procedure described by [F. D. Ryan, Phys. Rev. D {\bf 52} 5707 (1995)] and [T. P. Sotiriou and T. A. Apostolatos, Phys. Rev. D {\bf 71} 044005 (2005)].