Solution of the Einstein-Maxwell equations for two unequal spinning sources in equilibrium

Abstract

Starting with the basic equations developed by Israel and Wilson, and Perjes, we give the explicit form for the axially symmetric metric corresponding to two charged spinning Kerr-Newman sources in equilibrium under their mutual electromagnetic and gravitational forces. Spin directions can be parallel or antiparallel along the symmetry axis, and arbitrary spin magnitudes and complex charge parameters are assumed throughout. We show that the condition for proper asymptotic behavior of the metric requires that the magnetic monopole moment of the charge distribution vanish (to within a duality transformation), possibly implying a deep connection between the asymptotic properties of the gravitational field and the absence of free magnetic monopoles. The requirement of regularity of the metric along the $z$ axis between the sources fixes the value of the imaginary (magnetic) part of the complex charge parameters.