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

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

Evaluation of antibacterial activity of Pisidium guajava and Gongronema Latifolium

Pisidium guajava and Gongronema latifolium are local plants used traditionally in south-eastern Nigeria to treat ailments such as cough, loss of appetite, malaria and stomach disorders. In this study, aqueous and ethanolic leaf extracts of P. guajava and G. latifolium were screened for antibacterial activity against two clinically isolated organisms of the gastrointestinal tract, Escherichia coli and Staphylococcus aureus. Results obtained show that leaf extracts of both plants possess significant antibacterial activities against the two isolates. Ethanolic extracts showed more inhibitory effect compared to the aqueous extracts. Extracts of P. guajava exhibited higher inhibitory effect than that of G. latifolium. The diameter of zones of inhibition by the leaf extracts of P. guajava was 8 - 16 mm and 14 - 21 mm respectively for the aqueous and ethanolic extracts. The minimum inhibitory concentrations (MICs) were 5.0 and 0.625 mg ml-1 respectively for the aqueous and ethanolic extracts of P. guajava. For the extracts of G. latifolium, the diameter of zones of inhibition was between 6 and 10 mm while MICs were 10.0 and 2.5 mg ml-1 respectively for the aqueous and ethanolic extract

The Geometry of Warped Product Singularities

In this article the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.Comment: 14 page