Non-axisymmetric configurations in the post-Newtonian Approximation to General Relativity

TL;DR

This paper develops a first-order post-Newtonian approximation for Dedekind ellipsoids using surface-adapted ellipsoidal coordinates, aiming to extend to higher orders in general relativity.

Contribution

It introduces a novel method employing surface-adapted ellipsoidal coordinates for post-Newtonian approximation of Dedekind ellipsoids, advancing the modeling of non-axisymmetric configurations.

Findings

First-order PN approximation achieved for Dedekind ellipsoids.

Method sets foundation for higher-order post-Newtonian calculations.

Enhances understanding of non-axisymmetric equilibrium shapes in GR.

Abstract

We use surface adapted ellipsoidal coordinates to obtain a first order post-Newtonian (PN) approximation to Dedekind ellipsoids with the intention of proceeding to higher orders.