Symmetries of the stationary Einstein–Maxwell field equations. III

Abstract

We further investigate the infinite hierarchy of potentials and nonlinear symmetry transformations given in a previous paper. We outline a general method of explicitly calculating the potentials for a given spacetime. We show that some of the transformations can be exponentiated to finite values of their parameters, making them available as a means of generating new solutions. In particular, we show how our transformations may be used to generate all static solutions (including Schwarzschild), starting from nothing but flat space.