Exact solutions of the Einstein equations with sources from linearized solutions

It is shown that if (g(mu nu), F-mu nu) is an exact solution of the Einstein-Maxwell equations and l(mu) is a principal null direction of F-mu nu then (g(mu nu) + 2Hl(mu)l(nu), F-mu nu) is also an exact solution of the Einstein-Maxwell, equations if and only if (2Hl(mu)l(nu), 0) satisfies the Einstein-Maxwell equations linearized about (g(mu nu), F-mu nu). It is also shown that an analogous result applies in the case of the Einstein-Weyl equations if l(mu) is parallel to the flux vector of the neutrino field. (C) 1996 American Institute of Physics.