A rotating three component perfect fluid source and its junction with empty space-time

TL;DR

This paper develops rotating interior solutions for Einstein's equations using ellipsoidal coordinates, revealing an anisotropic three-component perfect fluid as the source, and connects these to the Kerr vacuum solution.

Contribution

It introduces a method to generate rotating interior solutions with an anisotropic three-component perfect fluid source, extending static perfect fluid models to include rotation.

Findings

Rotating solutions are derived from the Kerr metric in ellipsoidal coordinates.

The interior source is identified as an anisotropic three-component perfect fluid.

The Schwarzschild interior solution is recovered as a special case.

Abstract

The Kerr solution for empty space-time is presented in an ellipsoidally symmetric coordinate system and it is used to produce generalised ellipsoidal metrics appropriate for the generation of rotating interior solutions of Einstein's equations. It is shown that these solutions are the familiar static perfect fluid cases commonly derived in curvature coordinates but now endowed with rotation. The resulting solutions are also discussed in the context of T-solutions of Einstein's equations and the vacuum T-solution outside a rotating source is presented. The interior source for these solutions is shown not to be a perfect fluid but rather an anisotropic three component perfect fluid for which the energy momentum tensor is derived. The Schwarzschild interior solution is given as an example of the approach.