Slowly rotating, compact fluid sources embedded in Kerr empty space-time

TL;DR

This paper models slowly rotating, compact fluid sources within Kerr spacetime, deriving Einstein's equations as differential equations and explicitly describing the boundary shape based on angular and physical parameters.

Contribution

It introduces a method to embed static fluid sources into Kerr spacetime with rotation, using Darmois junction conditions and quadratic angular velocity terms.

Findings

Explicit boundary shape in terms of sinusoidal functions

Differentiates boundary shape based on equation of state

Provides differential equations for rotating fluid sources

Abstract

Spherically symmetric static fluid sources are endowed with rotation and embedded in Kerr empty space-time up to an including quadratic terms in an angular velocity parameter using Darmois junction conditions. Einstein's equation's for the system are developed in terms of linear ordinary differential equations. The boundary of the rotating source is expressed explicitly in terms of sinusoidal functions of the polar angle which differ somewhat according to whether an equation of state exists between internal density and supporting pressure.