Nonlinear and perturbative evolution of distorted black holes: Odd-parity modes

We study fully nonlinear and perturbative evolutions of nonrotating black holes with odd-parity distortions. Perturbative methods proved to be useful in order to interpret the nonlinear results. In particular, they provided insight on the nonlinear dependence of the wave forms with the distortion parameter $Q_0,$ explaining it in terms of the multipole coupling. We also found an increase in the frequency of the wave forms in the nonlinear regime which results from the loss of a noticeable part of the initial total mass of the system to gravitational radiation producing effectively a drifting of the quasinormal frequencies. The nonlinear evolutions have been performed (and cross checked) with the 3D parallel code for numerical relativity, CACTUS, and an independent axisymmetric code MAGOR. The linearized ones using the Regge-Wheeler formalism.