, Volume 7, Issue 8, pp 669-680

A class of approximate stationary solutions of the Einstein-Maxwell equations

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Abstract

A class of approximate stationary solutions of the Einstein-Maxwell equations are obtained by expanding the metric in powers of a certain parameter and solving explicitly the first few orders in terms of four harmonic functions. These solutions, to the order considered, reduce to the Weyl, Bonnor, and Perjés-Israel-Wilson solutions, respectively, for suitable choice of the harmonic functions. They also contain a subclass that is asymptomatically flat and has realistic arbitrary spinning sources.