A Periodic Table for Black Hole Orbits

Understanding the dynamics around rotating black holes is imperative to the success of the future gravitational wave observatories. Although integrable in principle, test particle orbits in the Kerr spacetime can also be elaborate, and while they have been studied extensively, classifying their general properties has been a challenge. This is the first in a series of papers that adopts a dynamical systems approach to the study of Kerr orbits, beginning with equatorial orbits. We define a taxonomy of orbits that hinges on a correspondence between periodic orbits and rational numbers. The taxonomy defines the entire dynamics, including aperiodic motion, since every orbit is in or near the periodic set. A remarkable implication of this periodic orbit taxonomy is that the simple precessing ellipse familiar from planetary orbits is not allowed in the strong-field regime. Instead, eccentric orbits trace out precessions of multi-leaf clovers in the final stages of inspiral. Furthermore, for any black hole, there is some point in the strong-field regime past which zoom-whirl behavior becomes unavoidable. Finally, we sketch the potential application of the taxonomy to problems of astrophysical interest, in particular its utility for computationally intensive gravitational wave calculations.Comment: 42 pages, lots of figure

Brownian motion: a paradigm of soft matter and biological physics

This is a pedagogical introduction to Brownian motion on the occasion of the 100th anniversary of Einstein's 1905 paper on the subject. After briefly reviewing Einstein's work in its contemporary context, we pursue some lines of further developments and applications in soft condensed matter and biology. Over the last century Brownian motion became promoted from an odd curiosity of marginal scientific interest to a guiding theme pervading all of the modern (live) sciences.Comment: 30 pages, revie

Field equations in teleparallel spacetime: Einstein's Fernparallelismus approach towards unified field theory

A historical account of Einstein's 'Fernparallelismus' approach towards a unified field theory of gravitation and electromagnetism is given. In this theory, a space-time characterized by a curvature-free connection in conjunction with a metric tensor field, both defined in terms of a dynamical tetrad field, is investigated. The approach was pursued by Einstein in a number of publications that appeared in the period from summer 1928 until spring 1931. In the historical analysis special attention is given to the question of how Einstein tried to find field equations for the tetrads. We claim that it was the failure to find and justify a uniquely determined set of acceptable field equations which eventually led to Einstein's abandoning of this approach. We comment on some historical and systematic similarities between the 'Fernparallelismus' episode and the 'Entwurf' theory, i.e. the precursor theory of general relativity pursued by Einstein in the years 1912-1915.Comment: 47 page

Albert Einstein: a biography

Albert Einstein's achievements are not just milestones in the history of science; decades ago they became an integral part of the twentieth-century world in which we live. Like no other modern physicist he altered and expanded our understanding of nature. Like few other scholars, he stood fully in the public eye. In a world changing with dramatic rapidity, he embodied the role of the scientist by personal example. Albrecht Folsing, relying on previously unknown sources and letters, brings Einstein's "genius" into focus. Whereas former biographies, written in the tradition of the history of science, seem to describe a heroic Einstein who fell to earth from heaven, Folsing attempts to reconstruct Einstein's thought in the context of the state of research at the turn of the century. Thus, perhaps for the first time, Einstein's surroundings come to light

Neue Carbonylmetall-Komplexe von Aluminium, Gallium und Indium

Die Arbeit liefert eine Beschreibung der Synthese, Charakterisierung und beschichtungstechnischen Anwendung von Übergangsmetall-substituierten und -stabilisierten Aluminium-, Gallium- und Indiumverbindungen. Anhand der Metallkomplexe $(CO)_{n}M-E[(X)(L_{m})]$ wird die Reihe für E=Al, Ga, In, für X=Cl, Br, I, $CH_{3}$, für L=N-Donoren und für Cr, Mo, W sowie Fe systematisch vervollständigt

Fröbel'sche Kindergärten, oder, Beurtheilung der von Middendorff beschriebenen ersten Kindheitspflege

von J. Fölsin