Slowly, rotating non-stationary, fluid solutions of Einstein's equations and their match to Kerr empty space-time

TL;DR

This paper develops a method to match slowly rotating fluid solutions of Einstein's equations with the Kerr spacetime, applicable to various known non-rotating sources, and analyzes their rotational properties.

Contribution

It introduces a general approach to match slowly rotating fluid solutions to Kerr spacetime, extending previous models to include internal pressure and specific boundary conditions.

Findings

Match applies to known non-rotating fluid sources with zero pressure boundary surface.

Method determines differential angular velocity of rotating systems.

Analysis shows induced inertial frame rotation in these solutions.

Abstract

A general class of solutions of Einstein's equation for a slowly rotating fluid source, with supporting internal pressure, is matched using Lichnerowicz junction conditions, to the Kerr metric up to and including first order terms in angular speed parameter. It is shown that the match applies to any previously known non-rotating fluid source made to rotate slowly for which a zero pressure boundary surface exists. The method is applied to the dust source of Robertson-Walker and in outline to an interior solution due to McVittie describing gravitational collapse. The applicability of the method to additional examples is transparent. The differential angular velocity of the rotating systems is determined and the induced rotation of local inertial frame is exhibited.