A Class of Fourth Order Approximate Solutions of Stationary Exterior Fields of Einstein Maxwell Equations
A class of approximate solutions of stationary exterior fields of Einstein Maxwell (EM) 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. Previously these approximate solutions in closed form were found upto third order. In the present paper we obtain new fourth order equations and find their approximate solutions for the particular choice of the harmonic functions. The harmonic functions are so chosen that all the approximate solutions obtained are asymptotically flat. Here some relations obtained are claimed to be a 'laboratory' with which future attempts at exact solutions in terms of harmonic functions may be tested.