We present a systematic and robust approach to nonlinear gravitationalperturbations of vacuum spacetimes. This approach provides a basis for a theoryof nonlinear gravitational waves. In particular, we show that the system ofperturbative Einstein equations reduces at each perturbation order to two (foreach gravitational mode in 3 + 1 dimensions on which our study is focused)scalar wave equations, and then we show how the metric perturbations can beexplicitly obtained, once the solutions to these scalar wave equations areknown. These results show that the concept of polarization of a gravitationalwave does make sense also beyond the linear approximation.
展开▼
