A basic feature of linearized perturbation theory is that there
is no ``built-in'' indication of how good the approximation is.
But if one has results for a physical quantity to second order in
a perturbation parameter, then the difference between the results
of the first and second order theory is a quantitative indication
of the error in the perturbation calculation. From this point of
view second order perturbation theory is a practical tool for
calculations. Nevertheless, there remain many technical problems
in this approach, for example the gauge that should be
used [100,
50] and the amount of calculations. Thus second order perturbation
theory has turned out to be much more difficult than linearized
theory, but if one overcomes these difficulties second order
calculations will be a great deal easier than numerical
relativity. From this point of view we encourage work in this
direction. In particular, the perturbations of stellar
oscillations should be extended to second order, and the study of
the second order perturbations of black holes extended to the
Kerr case.