The Near-Linear Regime of Gravitational Waves in Numerical Relativity
  We report on a systematic study of the dynamics of gravitational waves in full 3D numerical relativity. We find that there exists an interesting regime in the parameter space of the wave configurations: a near-linear regime in which the amplitude of the wave is low enough that one expects the geometric deviation from flat spacetime to be negligible, but nevertheless where nonlinearities can excite unstable modes of the Einstein evolution equations causing the metric functions to evolve out of control. The implications of this for numerical relativity are discussed. 
Peter Anninos, Joan Masso, Edward Seidel, Wai-Mo Suen, Malcolm Tobias