Comparing results for a global metric from analytical perturbation theory and a numerical code

TL;DR

This paper compares analytical perturbation theory and a numerical code in modeling an axistationary spacetime with a rotating perfect fluid, analyzing errors and physical properties to validate the approaches.

Contribution

It provides a detailed comparison between analytical and numerical methods for modeling axistationary spacetimes with a specific equation of state.

Findings

Higher-order analytical approximations reduce metric errors.

Errors in multipole moments and physical properties are quantified.

Analytical and numerical results show good agreement within error margins.

Abstract

We compare the results obtained from analytical perturbation theory and the AKM numerical code for an axistationary spacetime built from matching a rotating perfect fluid interior with the equation of state $\epsilon-3p=4B$ of the simple MIT bag model and an asymptotically flat exterior. We discuss the behaviour of the error in the metric components of the analytical approximation going to higher orders. Additionally, we check and comment the errors in multipole moments, central pressure and some other physical properties of the spacetime.