An approximate global solution of Einstein's equations for a rotating two layers star

TL;DR

This paper develops an approximate global solution to Einstein's equations for a rotating star composed of two fluid layers with different equations of state, using weak-field and slow-rotation approximations.

Contribution

It introduces a novel two-layer star model with an approximate global solution to Einstein's equations considering rotation and different fluid layers.

Findings

Derived interior and exterior solutions in harmonic coordinates.

Matched solutions on pressure surfaces to form a global model.

Applied post-Minkowskian and slow-rotation approximations.

Abstract

We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple two layers star model: a self-gravitating ball built up by two layers of perfect fluid having different linear equation of state moving in a rigid motion pattern. Using the post-Min\-kows\-kian formalism (weak-field approximation) and considering rotation as a perturbation (slow-rotation approximation), we find approximate interior and exterior (asymptotically flat) solutions to this problem in harmonic coordinates. Interior and exterior solutions are matched, in the sense described by Lichnerowicz, on the surfaces of constant pressure, to obtain a global solution.