A unifying coordinate family for the Kerr-Newman metric

A new unified metric form is presented for the Kerr-Newman geometry. The new form is a generalization of the Boyer-Lindquist metric involving an arbitrary gauge function of the spheroidal radial variable. Each choice of the gauge function corresponds to a coordinate system including four of the most important coordinate systems for Kerr-Newman (Boyer-Lindquist, Kerr, Kerr-Schild and Doran coordinates). The representation is given in terms of a single Minkowski frame together with the gauge function. This Minkowski frame arises by boosting a static orthonormal frame which is adapted to spheroidal coordinates. Properties of the boost reflect the rotating nature of the Kerr-Newman solution including an identification of the angular velocities of the disk and the horizon matching previously known values obtained in other ways.