Twistor Actions for Integrable Systems

Summary: Under the action of the Geroch group, the Minkowski metric can be transformed into any vacuum metric with two commuting Killing vectors. This simplifies the problem of deriving vacuum metrics with two commuting Killing vectors to pure algebra. The authors use these facts to give a purely algebraic derivation of the Einstein-Rosen metric, which describes a cylindrical gravitational wave, with a straightforward extension to gravitational pulse waves.