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We consider the problem of evolving nonlinear initial data in the close limitregime. Metric and curvature perturbations of nonrotating black holes areequivalent to first perturbative order, but Moncrief waveform in the formercase and Weyl scalar $\psi_4$ in the later differ when nonlinearities arepresent. For exact Misner initial data (two equal mass black holes initially atrest), metric perturbations evolved via the Zerilli equation suffer of apremature break down (at proper separation of the holes $L/M\approx2.2$) whilethe exact Weyl scalar $\psi_4$ evolved via the Teukolsky equation keeps a verygood agreement with full numerical results up to $L/M\approx3.5$. We argue thatthis inequivalent behavior holds for a wider class of conformally flat initialdata than those studied here. We then discuss the relevance of these resultsfor second order perturbative computations and for perturbations to take overfull numerical evolutions of Einstein equations.Comment: 7 pages, 7 figure

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