Stationary axisymmetric interior metric for a charged perfect fluid source

Abstract

A stationary axisymmetric type-D solution of the Einstein equations coupled with an electromagnetic field and a rigidly rotating perfect fluid distribution of finite dimensions is presented. For vanishing fluid parameters, it reduces to the Carter [A] metric, which contains among others the Kerr–Newman solution. When the electromagnetic field is switched off, it reduces to the Wahlquist perfect fluid metric. The Debever–Penrose directions are geodesic, shear-free, twisting, and diverging. This solution belongs to the Wainwright class II. The expressions of the functions of other new solutions are also given.