### 7.2 Second order perturbations

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 [104, 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.