Perturbative evolution of nonlinear initial data for binary black holes: Zerilli vs. Teukolsky

We consider the problem of evolving nonlinear initial data in the close limit regime. Metric and curvature perturbations of nonrotating black holes are equivalent to first perturbative order, but Moncrief waveform in the former case and Weyl scalar $\psi_4$ in the later differ when nonlinearities are present. For exact Misner initial data (two equal mass black holes initially at rest), metric perturbations evolved via the Zerilli equation suffer of a premature break down (at proper separation of the holes $L/M\approx2.2$) while the exact Weyl scalar $\psi_4$ evolved via the Teukolsky equation keeps a very good agreement with full numerical results up to $L/M\approx3.5$. We argue that this inequivalent behavior holds for a wider class of conformally flat initial data than those studied here. We then discuss the relevance of these results for second order perturbative computations and for perturbations to take over full numerical evolutions of Einstein equations.Comment: 7 pages, 7 figure

Controlled ferrite content improves weldability of corrosion-resistant steel

Corrosion-resistant steel that adds restrictions on chemical composition to ensure sufficient ferrite content decreases the tendency of CRES to develop cracks during welding. The equations restricting composition are based on the Schaeffler constitution diagram

Some Thermodynamic Aspects of Black Holes and Singularities

We review and correct the classical critical exponents characterizing the transition from negative to positive black hole's heat capacity at high charge--angular momentum. We discuss the stability properties of black holes as a thermodynamic system in equilibrium with a radiation bath (canonical ensamble) by using the Helmholtz free energy potential. We finally analytically extend the analysis to negative mass holes and study its thermodynamical stability behavior.Comment: 16 pages, RevTeX, 5 compressed figure