Einstein-Maxwell Spacetime with Two Commuting Spacelike Killing Vector Fields and Newman-Penrose Formalism

Abstract

Einstein-Maxwell spacetimes endowed with twocommuting spacelike Killing vector fields areconsidered. Subject to the hypotheses that one of thetwo null geodesic congruence orthogonal to thetwo-surface generated by the two commuting spacelikeKilling vector fields is shearfree and theelectromagnetic field is non null, it is shown that,with a specific choice of null tetrad, theNewman-Penrose equations together with the Maxwell equations for theclass of spacetime considered may be reduced to asecond-order ode of Sturm-Liouville type, from whichexact solutions of the class of spacetimes consideredmay be constructed. Examples of exact solutions arethen given. Exact solutions with distribution-valuedWeyl curvature describing the scattering ofelectromagnetic shock wave with gravitational impulsiveor shock wave of variable polarisation are also constructed.