We study the even-parity l = 2 perturbations of a Schwarzschild black
hole to second order. The Einstein equations can be reduced to a singl
e linear wave equation with a potential and a source term. The source
term is quadratic in terms of the first-order perturbations. This prov
ides a formalism to address the validity of many first-order calculati
ons of interest in astrophysics.