Bäcklund Transformation for the Ernst Equation of General Relativity

A Bäcklund transformation for the Ernst equation arising in general relativity in connection with several physical problems is derived, using the pseudopotential method of Wahlquist and Estabrook. A prolongation structure is also constructed, using a method of writing the equations in terms of differential forms, and an equation in the spirit of Lax is constructed, somewhat different from that given by Maison. Possible uses of the Bäcklund transformation to generate new solutions are mentioned.