On generation of solutions of Einstein’s equations

Abstract

The equations for two‐Killing‐vector solutions of Einstein’s equations are looked at from the point of view of the Lagrangian formalism. The original Lagrangian, written in terms of the metric, will undergo a Legendre transformation leading to the Ernst Lagrangian and from there by the same procedure to others. So one gets a sequence of Lagrangians, and by performing an invariance transformation at each step one obtains new solutions of Einstein’s equations. A convenient method for dealing with Lagrangians quadratic in the velocities is outlined.