Material Sources for the Kerr Metric

The Kerr metric is a vacuum solution of the Einstein field equations which appears to be the field exterior to some axially symmetric, rotating body. A method based on Synge's g method (guess g_μν and calculate T_μν) is given for constructing interior solutions of the field equations which describe rotating, nonperfect-fluid bodies which might serve as sources of the Kerr metric. Finally, an argument is given which indicates that reasonable perfect-fluid---type solutions which might serve as sources of the Kerr metric may not exist.