The shadow of a collapsing dark star

The shadow of a black hole is usually calculated, either analytically or numerically, on the assumption that the black hole is eternal, i.e., that it has existed for all time. Here we ask the question of how this shadow comes about in the course of time when a black hole is formed by gravitational collapse. To that end we consider a star that is spherically symmetric, dark and non-transparent and we assume that it begins, at some instant of time, to collapse in free fall like a ball of dust. We analytically calculate the dependence on time of the angular radius of the shadow, first for a static observer who is watching the collapse from a certain distance and then for an observer who is falling towards the centre following the collapsing star.     

Minimizing Side Product Formation in Alkyne Functionalization of Ruthenium Complexes by Introduction of Protecting Groups

The synthesis of alkyne functionalized bipyridine ruthenium complexes are reported. The improved synthetic approach through application of stable protecting groups prevents formation of possible side products while facilitating purification. By applying copper-catalysed azide-alkyne cycloaddition reactions (CuAAC) pyrene units with flexible alkyl linkers are introduced at the periphery of the complex, opening up various applications including surface immobilization and DNA intercalation. All complexes are characterized structurally as well as photophysically, especially regarding the influence of the introduced alkyne and triazolyl substituents on their photophysical behavior.     

Synthesis and biological evaluation of 3-aryltyramines as fragments binding to BACE-1 and BACE-2

3-Aryltyramines were prepared in one single step from tyramine and various arenediazonium salts by radical arylation. Binding as well as enzyme inhibition data of the 14 compounds do not prove true interaction with BACE-1. In contrast, with BACE-2 inhibition and binding could be confirmed indicating that 3-aryltyramines are potential starting points for a drug discovery effort.     

A Hybrid Ring‐Opening Metathesis Polymerization Catalyst Based on an Engineered Variant of the β‐Barrel Protein FhuA

A β‐barrel protein hybrid catalyst was prepared by covalently anchoring a Grubbs–Hoveyda type olefin metathesis catalyst at a single accessible cysteine amino acid in the barrel interior of a variant of β‐barrel transmembrane protein ferric hydroxamate uptake protein component A (FhuA). Activity of this hybrid catalyst type was demonstrated by ring‐opening metathesis polymerization of a 7‐oxanorbornene derivative in aqueous solution.