The GHP conformai Killing equations and their integrability conditions,with application to twisting type N vacuum spacetimes

The conformai Killing equations in resolved form and their first and second integrability conditions are obtained in the compact spin coefficient formalism for arbitrary spacetimes. To facilitate calculations an operatorL is introduced which agrees with the Lie derivative only when operating on quantities with GHP weights (0,0). The resulting equations are used to find the conditions for the existence of a two dimensional non-Abelian group of homothetic motions in a twisting typeN vacuum spacetime. The equivalence of two such sets of metrics is established, metrics that were recently the subject of independent investigations by Herlt on the one hand and by Ludwig and Yu on the other.