Perturbative evolution of nonlinear initial data for binary black holes: Zerilli versus Teukolsky equation

We consider the problem of evolving nonlinear initial data in the close limit regime. For exact Misner initial data (two equal mass black holes initially at rest), metric perturbations evolved via the Zerilli equation suffer from a premature breakdown (at a proper separation of the holes $L/M\approx 2.2)$ while we find that the exact Weyl scalar ${\psi }_4$ evolved via the Teukolsky equation keeps very good agreement with the full numerical results up to $L/M\approx \mathrm{3.5.}$ Metric and curvature perturbations of nonrotating black holes are equivalent to first perturbative order, but the Moncrief waveform in the former case and the Weyl scalar ${\psi }_4$ in the latter differ when nonlinearities are present. We argue that this inequivalent behavior holds for a wider class of conformally flat initial data.