Black Hole Shadows and Invariant Phase Space Structures

Utilizing concepts from dynamical systems theory, we demonstrate how the existence of light rings, or fixed points, in a spacetime will give rise to families of periodic orbits and invariant manifolds in phase space. It is shown that these structures define the shape of the black hole shadow as well as a number of salient features of the spacetime lensing. We illustrate this through the analysis of lensing by a hairy black hole.Comment: 6 page

A differential algebra based importance sampling method for impact probability computation on Earth resonant returns of Near Earth Objects

A differential algebra based importance sampling method for uncertainty propagation and impact probability computation on the first resonant returns of Near Earth Objects is presented in this paper. Starting from the results of an orbit determination process, we use a differential algebra based automatic domain pruning to estimate resonances and automatically propagate in time the regions of the initial uncertainty set that include the resonant return of interest. The result is a list of polynomial state vectors, each mapping specific regions of the uncertainty set from the observation epoch to the resonant return. Then, we employ a Monte Carlo importance sampling technique on the generated subsets for impact probability computation. We assess the performance of the proposed approach on the case of asteroid (99942) Apophis. A sensitivity analysis on the main parameters of the technique is carried out, providing guidelines for their selection. We finally compare the results of the proposed method to standard and advanced orbital sampling techniques

Long term nonlinear propagation of uncertainties in perturbed geocentric dynamics using automatic domain splitting

Current approaches to uncertainty propagation in astrodynamics mainly refer tolinearized models or Monte Carlo simulations. Naive linear methods fail in nonlinear dynamics, whereas Monte Carlo simulations tend to be computationallyintensive. Differential algebra has already proven to be an efficient compromiseby replacing thousands of pointwise integrations of Monte Carlo runs with thefast evaluation of the arbitrary order Taylor expansion of the flow of the dynamics. However, the current implementation of the DA-based high-order uncertainty propagator fails in highly nonlinear dynamics or long term propagation. We solve this issue by introducing automatic domain splitting. During propagation, the polynomial of the current state is split in two polynomials when its accuracy reaches a given threshold. The resulting polynomials accurately track uncertainties, even in highly nonlinear dynamics and long term propagations. Furthermore, valuable additional information about the dynamical system is available from the pattern in which those automatic splits occur. From this pattern it is immediately visible where the system behaves chaotically and where its evolution is smooth. Furthermore, it is possible to deduce the behavior of the system for each region, yielding further insight into the dynamics. In this work, the method is applied to the analysis of an end-of-life disposal trajectory of the INTEGRAL spacecraft

Leptonic and Semileptonic Decays of Pseudoscalar Mesons

We employ the relativistic constituent quark model to give a unified description of the leptonic and semileptonic decays of pseudoscalar mesons (\pi, K, D, D_s, B, B_s). The calculated leptonic decay constants and form factors are found to be in good agreement with available experimental data and other approaches. We reproduce the results of spin-flavor symmetry in the heavy quark limit.Comment: 12 pages LaTeX (elsart.sty) + 4 figures; added references, to appear in Phys. Lett.

The mitochondrial genome of the venomous cone snail conus consors

Cone snails are venomous predatory marine neogastropods that belong to the species-rich superfamily of the Conoidea. So far, the mitochondrial genomes of two cone snail species (Conus textile and Conus borgesi) have been described, and these feed on snails and worms, respectively. Here, we report the mitochondrial genome sequence of the fish-hunting cone snail Conus consors and describe a novel putative control region (CR) which seems to be absent in the mitochondrial DNA (mtDNA) of other cone snail species. This possible CR spans about 700 base pairs (bp) and is located between the genes encoding the transfer RNA for phenylalanine (tRNA-Phe, trnF) and cytochrome c oxidase subunit III (cox3). The novel putative CR contains several sequence motifs that suggest a role in mitochondrial replication and transcription

Multiple shadows from distorted static black holes

We study the local shadow of the Schwarzschild black hole with a quadrupole distortion and the influence of the external gravitational field on the photon dynamics. The external matter sources modify the light ring structure and lead to the appearance of multiple shadow images. In the case of negative quadrupole moments we identify the most prominent mechanism causing multiple shadow formation. Furthermore, we obtain a condition under which this mechanism can be realized. This condition depends on the quadrupole moment, but also on the position of the observer and the celestial sphere.Comment: 18 pages, 14 figure