Generalization of the Hauser-Ernst formalism for two-dimensional reduced Einstein abelian gauge field equations

Abstract

Recently the Hauser-Ernst formalism has played an important role in the discussion of the Virasoro symmetry in the two-dimensional reduced gravity theory. In this Letter we generalize the Hauser-Ernst formalism to the Einstein abelian gauge field equations when the spacetime possesses two commuting Killing vectors. Using this formalism, it is effective to investigate the Kac-Moody symmetry and, in particular, the Virasoro symmetry, which can be used to induced new solutions from the old one. We then provide an example concerning the derivation of a six-parameter generalization of a three-parameter family of colliding wave solutions found by Ernst, García and Hauser.