The complete set of solutions of the geodesic equations in the space-time of a Schwarzschild black hole pierced by a cosmic string

We study the geodesic equations in the space-time of a Schwarzschild black hole pierced by an infinitely thin cosmic string and give the complete set of analytical solutions of these equations for massive and massless particles, respectively. The solutions of the geodesic equations can be classified according to the particle's energy and angular momentum, the ratio between the component of the angular momentum aligned with the axis of the string and the total angular momentum, the deficit angle of the space-time and as well the horizon radius (or mass) of the black hole. For bound orbits of massive test particles we calculate the perihelion shift, we discuss light deflection and comment on the Newtonian limit.Comment: 21 pages; section 3 shortened, references added; accepted for publication in Phys. Rev.

Functional morphology and efficiency of the antenna cleaner in Camponotus rufifemur ants

Contamination of body surfaces can negatively affect many physiological functions. Insects have evolved different adaptations for removing contamination, including surfaces that allow passive self-cleaning and structures for active cleaning. Here, we study the function of the antenna cleaner in Camponotus rufifemur ants, a clamp-like structure consisting of a notch on the basitarsus facing a spur on the tibia, both bearing cuticular ’combs’ and ’brushes’. The ants clamp one antenna tightly between notch and spur, pull it through, and subsequently clean the antenna cleaner itself with the mouthparts. We simulated cleaning strokes by moving notch or spur over antennae contaminated with fluorescent particles. The notch removed particles more efficiently than the spur, but both components eliminated >60% of the particles with the first stroke. Ablation of bristles, brush and comb strongly reduced the efficiency, indicating that they are essential for cleaning. To study how comb and brush remove particles of different sizes, we contaminated antennae of living ants, and anaesthetized them immediately after they had performed the first cleaning stroke. Different sized beads were trapped in distinct zones of the notch, consistent with the gap widths between cuticular outgrowths. This suggests that the antenna cleaner operates like a series of sieves that remove the largest objects first, followed by smaller ones, down to the smallest particles that get caught by adhesion.To AH: Research grant from the Konrad-Adenauer-Foundation To DL: Research grant from the Cusanuswerk To WF: UK Biotechnology and Biological Sciences Research Council (BB/I008667/1)This is the final version of the article. It first appeared from RSC via http://dx.doi.org/10.1098/rsos.15012

Analytic treatment of complete and incomplete geodesics in Taub-NUT space-times

We present the complete set of analytical solutions of the geodesic equation in Taub-NUT space-times in terms of the Weierstrass elliptic function. We systematically study the underlying polynomials and characterize the motion of test particles by its zeros. Since the presence of the "Misner string" in the Taub-NUT metric has led to different interpretations, we consider these in terms of the geodesics of the space-time. In particular, we address the geodesic incompleteness at the horizons discussed by Misner and Taub, and the analytic extension of Miller, Kruskal and Godfrey, and compare with the Reissner-Nordstr\"om space-time.Comment: 22 pages, 14 figures, accepted for publication in PR

Particle motion in the field of a five-dimensional charged black hole

In this paper, we have investigated the geodesics of neutral particles near a five-dimensional charged black hole using a comparative approach. The effective potential method is used to determine the location of the horizons and to study radial and circular trajectories. This also helps us to analyze the stability of radial and circular orbits. The radius of the innermost stable circular orbits have also been determined. Contrary to the case of massive particles for which, the circular orbits may have up to eight possible values of specific radius, we find that the photons will only have two distinct values for the specific radii of circular trajectories. Finally we have used the dynamical systems analysis to determine the critical points and the nature of the trajectories for the timelike and null geodesics.Comment: 15 pages, accepted for publication in Astrophysics and Space Scienc

Geodesic motion in the space-time of a cosmic string

We study the geodesic equation in the space-time of an Abelian-Higgs string and discuss the motion of massless and massive test particles. The geodesics can be classified according to the particles energy, angular momentum and linear momentum along the string axis. We observe that bound orbits of massive particles are only possible if the Higgs boson mass is smaller than the gauge boson mass, while massless particles always move on escape orbits. Moreover, neither massive nor massless particles can ever reach the string axis for non-vanishing angular momentum. We also discuss the dependence of light deflection by a cosmic string as well as the perihelion shift of bound orbits of massive particles on the ratio between Higgs and gauge boson mass and the ratio between symmetry breaking scale and Planck mass, respectively.Comment: 20 pages including 14 figures; v2: references added, discussion on null geodesics extended, numerical results adde