Revising the multipole moments of numerical spacetimes, and its consequences

TL;DR

This paper clarifies the correct method to extract multipole moments from numerical spacetimes, improving the accuracy of analytic metric representations and impacting astrophysical modeling.

Contribution

It identifies a widespread misconception in reading multipole moments from numerical metrics and provides corrected procedures to enhance analytic descriptions.

Findings

Corrected method for extracting multipole moments from numerical metrics

Improved accuracy of analytic metrics using the corrected moments

Enhanced efficiency in modeling astrophysical objects

Abstract

Identifying the relativistic multipole moments of a spacetime of an astrophysical object that has been constructed numerically is of major interest, both because the multipole moments are intimately related to the internal structure of the object, and because the construction of a suitable analytic metric that mimics a numerical metric should be based on the multipole moments of the latter one, in order to yield a reliable representation. In this note we show that there has been a widespread delusion in the way the multipole moments of a numerical metric are read from the asymptotic expansion of the metric functions. We show how one should read correctly the first few multipole moments (starting from the quadrupole mass-moment), and how these corrected moments improve the efficiency of describing the metric functions with analytic metrics that have already been used in the literature, as well as other consequences of using the correct moments.