Perturbations of solutions of the Einstein-Maxwell equations with a null background electromagnetic field

Expressions for the complete metric and vector potential perturbations of solutions of the Einstein-Maxwell equations with a null background electromagnetic field in terms of two complex scalar potentials are derived using Wald's method of adjoint operators. The perturbations of the Bell-Szekeres solution, in the regions prior to the collision of the plane-fronted waves, are obtained by this approach. We find that there exist nontrivial u-independent perturbations (where partial derivative(u) defines the direction of propagation of the colliding wave) which, when the electromagnetic perturbation vanishes, are exact solutions of the Einstein-Maxwell equations. (C) 1996 American Institute of Physics.