Fermion perturbations in string theory black holes

In this paper we study fermion perturbations in four-dimensional black holes of string theory, obtained either from a non-extreme configuration of three intersecting five-branes with a boost along the common string or from a non-extreme intersecting system of two two-branes and two five-branes. The Dirac equation for the massless neutrino field, after conformal re-scaling of the metric, is written as a wave equation suitable to study the time evolution of the perturbation. We perform a numerical integration of the evolution equation, and with the aid of Prony fitting of the time-domain profile, we calculate the complex frequencies that dominate the quasinormal ringing stage, and also determine these quantities by the semi-analytical sixth-order WKB method. We also find numerically the decay factor of fermion fields at very late times, and show that the falloff is identical to those showing for massless fields in other four-dimensional black hole spacetimes.

Health in Brazil 6 Health conditions and health-policy innovations in Brazil: the way forward

Brazil is a large complex country that is undergoing rapid economic, social, and environmental change In this Series of six articles, we have reported important improvements in health status and life expectancy, which can be ascribed largely to progress in social determinants of health and to implementation of a comprehensive national health system with strong social participation. Many challenges remain, however. Socioeconomic and regional disparities are still unacceptably large, reflecting the fact that much progress is still needed to improve basic living conditions for a large proportion of the population. New health problems arise as a result of urbanisation and social and environmental change, and some old health issues remain unabated. Administration of a complex, decentralised public-health system, in which a large share of services is contracted out to the private sector, together with many private insurance providers, inevitably causes conflict and contradiction. The challenge is ultimately political, and we conclude with a call for action that requires continuous engagement by Brazilian society as a whole in securing the right to health for all Brazilian people.