Retarded coordinates based at a world line, and the motion of a small black hole in an external universe

In the first part of this article I present a system of retarded coordinates based at an arbitrary world line of an arbitrary curved spacetime. The retarded-time coordinate labels forward light cones that are centered on the world line, the radial coordinate is an affine parameter on the null generators of these light cones, and the angular coordinates are constant on each of these generators. The spacetime metric in the retarded coordinates is displayed as an expansion in powers of the radial coordinate and expressed in terms of the world line's acceleration vector and the spacetime's Riemann tensor evaluated at the world line. The formalism is illustrated in two examples, the first involving a comoving world line of a spatially-flat cosmology, the other featuring an observer in circular motion in the Schwarzschild spacetime. The main application of the formalism is presented in the second part of the article, in which I consider the motion of a small black hole in an empty external universe. I use the retarded coordinates to construct the metric of the small black hole perturbed by the tidal field of the external universe, and the metric of the external universe perturbed by the presence of the black hole. Matching these metrics produces the MiSaTaQuWa equations of motion for the small black hole.Comment: 20 pages, revtex4, 2 figure

The Role of Demography in the Transition to Sustainable Societies

Currently, although the global population has surpassed 7.5 billion and continues to increase in about 80 million each year, attention to demography is almost absent in most of the studies and publications related to the current situation of planetary emergency and the necessary transition to sustainable societies. For this reason, our first aim in this paper has been to discuss if this current lack of attention to demography is justified or not. With this purpose, we begin considering the scientific meaning of Sustainability, in order to overlay distorted and impoverish views of this concept that may hinder our study. Then, we analyse the reasons given by experts for and against the incidence of demographic growth in the current unsustainable situation of planetary emergency. Finally, we present proposals to face the ensemble of interconnected socio-environmental problems (including demographic evolution), to make possible an appropriate transition to sustainable societies. Aunque la población mundial ha sobrepasado los 7500 millones y continúa aumentando anualmente en alrededor de 80 millones, la atención a la demografía está hoy prácticamente ausente en la mayoría de los estudios y publicaciones acerca de la actual situación de emergencia planetaria y la necesidad de una transición a sociedades sostenibles. Con el propósito de analizar si esta falta de atención a la demografía está o no justificada, en esta contribución comenzamos discutiendo el significado científico de Sostenibilidad socioambiental, para evitar concepciones distorsionadas y empobrecidas de este concepto que pueden dificultar dicho análisis. A continuación estudiaremos las razones dadas por distintos expertos a favor y en contra de la incidencia del crecimiento demográfico en la insostenible situación actual de emergencia planetaria. Finalmente presentamos propuestas para hacer frente al conjunto de problemas estrechamente interconectados - incluido el problema demográfico - que caracterizan dicha situación, para hacer así posible una adecuada transición a sociedades sostenibles

National Institutes of Health Career Development Awards for Cardiovascular Physician-Scientists: Recent Trends and Strategies for Success

Nurturing the development of cardiovascular physician-scientist investigators is critical for sustained progress in cardiovascular science and improving human health. The transition from an inexperienced trainee to an independent physician-scientist is a multifaceted process requiring a sustained commitment from the trainee, mentors, and institution. A cornerstone of this training process is a career development (K) award from the National Institutes of Health (NIH). These awards generally require 75% of the awardee's professional effort devoted to research aims and diverse career development activities carried out in a mentored environment over a 5-year period. We report on recent success rates for obtaining NIH K awards, provide strategies for preparing a successful application and navigating the early career period for aspiring cardiovascular investigators, and offer cardiovascular division leadership perspectives regarding K awards in the current era. Our objective is to offer practical advice that will equip trainees considering an investigator path for success

Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note: updated version of arXiv:gr-qc/050809