Towards a theory of nonlinear gravitational waves: A systematic approach to nonlinear gravitational perturbations in the vacuum

摘要

We present a systematic and robust approach to nonlinear gravitational perturbations of vacuumspacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, weshow that the system of perturbative Einstein equations reduces at each perturbation order to two (for eachgravitational mode in 3 + 1 dimensions on which our study is focused) scalar wave equations, and then weshow how the metric perturbations can be explicitly obtained, once the solutions to these scalar waveequations are known. These results show that the concept of polarization of a gravitational wave does makesense also beyond the linear approximation.