Comparison of metrics obtained with analytic perturbation theory and a numerical code

TL;DR

This paper compares analytic perturbation theory metrics with numerical solutions for rotating perfect fluid spacetimes, assessing their differences inside the source, at infinity, and on the matching surface.

Contribution

It evaluates the accuracy of the CMMR post-Minkowskian approximation against a spectral numerical code for rotating fluid bodies.

Findings

Good agreement outside the source

Differences observed near the matching surface

Insights into the global validity of the perturbation scheme

Abstract

We compare metrics obtained through analytic perturbation theory with their numerical counterparts. The analytic solutions are computed with the CMMR post-Minkowskian and slow rotation approximation due to Cabezas et al. (2007) for an asymptotically flat stationary spacetime containing a rotating perfect fluid compact source. The same spacetime is studied with the AKM numerical multi-domain spectral code (Ansorg et al., 2002,2003). We then study their differences inside the source, near the infinity and in the matching surface, or equivalently, the global character of the analytic perturbation scheme.