Symmetries of the stationary Einstein–Maxwell equations. IV. Transformations which preserve asymptotic flatness

We give a series of transformations βk, k=0,1,... which may be used to generate new stationary axially-symmetric vacuum solutions from ones already known. These transformations have the important property of preserving asymptotic flatness. As one example of their use, we show how to generate the Kerr metric from Schwarzschild. As a second example, we generate a new five-parameter vacuum solution which contains the δ=2 Tomimatsu–Sato solution as a special case.