Abstracto
- It is shown that if (gμν,Fμν) is an exact solution of the Einstein–Maxwell equations and lμ is a principal null direction of Fμν then (gμν+2Hlμlν,Fμν) is also an exact solution of the Einstein–Maxwell equations if and only if (2Hlμlν,0) satisfies the Einstein–Maxwell equations linearized about (gμν,Fμν). It is also shown that an analogous result applies in the case of the Einstein–Weyl equations if lμ is parallel to the flux vector of the neutrino field.