Geodesic equations and algebro-geometric methods

For an investigation of the physical properties of gravitational fields the observation of massive test particles and light is very useful. The characteristic features of a given space-time may be decoded by studying the complete set of all possible geodesic motions. Such a thorough analysis can be accomplished most effectively by using analytical methods to solve the geodesic equation. In this contribution, the use of elliptic functions and their generalizations for solving the geodesic equation in a wide range of well known space-times, which are part of the general Pleba\'nski-Demia\'nski family of solutions, will be presented. In addition, the definition and calculation of observable effects like the perihelion shift will be presented and further applications of the presented methods will be outlined.Comment: 8 pages, no figures; based on presentation at the conference "Relativity and Gravitation: 100 Years after Einstein in Prague," Prague, 2012. Relativity and Gravitation, volume 157 of Springer Proceedings in Physics, p 91. Springer International Publishing, 201

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.

Analytical solution of the geodesic equation in Kerr-(anti) de Sitter space-times

The complete analytical solutions of the geodesic equations in Kerr-de Sitter and Kerr-anti-de Sitter space-times are presented. They are expressed in terms of Weierstrass elliptic p, zeta, and sigma functions as well as hyperelliptic Kleinian sigma functions restricted to the one-dimensional theta-divisor. We analyze the dependency of timelike geodesics on the parameters of the space-time metric and the test-particle and compare the results with the situation in Kerr space-time with vanishing cosmological constant. Furthermore, we systematically can find all last stable spherical and circular orbits and derive the expressions of the deflection angle of flyby orbits, the orbital frequencies of bound orbits, the periastron shift, and the Lense-Thirring effect.Comment: 18 pages, 11 figure

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

Lense-Thirring Precession in Pleba\'nski-Demia\'nski spacetimes

An exact expression of Lense-Thirring precession rate is derived for non-extremal and extremal Pleba\'nski-Demia\'nski spacetimes. This formula is used to find the exact Lense-Thirring precession rate in various axisymmetric spacetimes, like: Kerr, Kerr-Newman, Kerr-de Sitter etc. We also show, if the Kerr parameter vanishes in Pleba\'nski-Demia\'nski(PD) spacetime, the Lense-Thirring precession does not vanish due to the existence of NUT charge. To derive the LT precession rate in extremal Pleba\'nski-Demia\'nski we first derive the general extremal condition for PD spacetimes. This general result could be applied to get the extremal limit in any stationary and axisymmetric spacetimes.Comment: 9 pages, Some special modifications are mad

Nucleonic resonance excitations with linearly polarized photon in γp→ωp\gamma p\to \omega p

In this work, an improved quark model approach to the $\omega$ meson photo-production with an effective Lagrangian is presented. The {\it t}-channel {\it natural}-parity exchange is taken into account through the Pomeron exchange, while the {\it unnatural}-parity exchange is described by the $\pi^0$ exchange. With a very limited number of parameters, the available experimental data in the low energy regime can be consistently accounted for. We find that the beam polarization observables show sensitivities to some {\it s}-channel individual resonances in the $SU(6)\otimes O(3)$ quark model symmetry limit. Especially, the two resonances $P_{13}(1720)$ and $F_{15}(1680)$, which belong to the representation $[{\bf 56, ^2 8}, 2, 2, J]$, have dominant contributions over other excited states. Concerning the essential motivation of searching for "missing resonances" in meson photo-production, this approach provides a feasible framework, on which systematic investigations can be done.Comment: 16 pages, Revtex, 9 eps figures, to appear in PR

Co-design with aligned and non-aligned knowledge partners: implications for research and coproduction of sustainable food systems

We discuss two different strategies to initiate a process of identifying a focused sustainability challenge, and co-defining and co-designing alternative pathways to more sustainable food systems. One strategy was based on working with a relatively closely aligned network of private sector, civil society and academic organisations, whilst the other involved working with a more plural, non-aligned group, ranging from representatives of agricultural social movements, through to the domestic seed industry and government officials, to academic agronomists. This paper reflects on the distinct benefits and challenges involved in each strateg

The Pioneer Anomaly

Radio-metric Doppler tracking data received from the Pioneer 10 and 11 spacecraft from heliocentric distances of 20-70 AU has consistently indicated the presence of a small, anomalous, blue-shifted frequency drift uniformly changing with a rate of ~6 x 10^{-9} Hz/s. Ultimately, the drift was interpreted as a constant sunward deceleration of each particular spacecraft at the level of a_P = (8.74 +/- 1.33) x 10^{-10} m/s^2. This apparent violation of the Newton's gravitational inverse-square law has become known as the Pioneer anomaly; the nature of this anomaly remains unexplained. In this review, we summarize the current knowledge of the physical properties of the anomaly and the conditions that led to its detection and characterization. We review various mechanisms proposed to explain the anomaly and discuss the current state of efforts to determine its nature. A comprehensive new investigation of the anomalous behavior of the two Pioneers has begun recently. The new efforts rely on the much-extended set of radio-metric Doppler data for both spacecraft in conjunction with the newly available complete record of their telemetry files and a large archive of original project documentation. As the new study is yet to report its findings, this review provides the necessary background for the new results to appear in the near future. In particular, we provide a significant amount of information on the design, operations and behavior of the two Pioneers during their entire missions, including descriptions of various data formats and techniques used for their navigation and radio-science data analysis. As most of this information was recovered relatively recently, it was not used in the previous studies of the Pioneer anomaly, but it is critical for the new investigation.Comment: 165 pages, 40 figures, 16 tables; accepted for publication in Living Reviews in Relativit

Vitis vinifera lipoxygenase loxA is an allosteric dimer activated by lipidic surfaces

Lipoxygenases catalyze the peroxidation of poly-unsaturated fatty acid chains either free or esterified in membrane lipids. Vitis vinifera LoxA is transcriptionally induced at ripening onset and localizes at the inner chloroplast membrane where it is responsible for galactolipid regiospecific mono- and di-peroxidation. Here we present a kinetic and structural characterization of LoxA. Our X-ray structures reveal a constitutive dimer with detergent induced conformational changes affecting substrate binding and catalysis. In a closed conformation, a LID domain prevents substrate access to the catalytic site by steric hindrance. Detergent addition above the CMC destabilizes the LID and opens the dimer with both catalytic sites accessible from the same surface framed by the PLAT domains. As a consequence, detergent molecules occupy allosteric sites in the PLAT/catalytic domain interface. These structural changes are mirrored by increased enzymatic activity and positive cooperativity when the substrate is provided in micelles. The ability to interact with micelles is lost upon dimer destabilization by site-directed mutagenesis as assessed by tryptophan fluorescence. Our data allow to propose a model for protein activation at the membrane, classifying LoxA as an interfacial enzyme acting on fatty acid chains directly from the membrane similar to mammalian 15-LOX and 5-LOX

Structure of the pre-60S ribosomal subunit with nuclear export factor Arx1 bound at the exit tunnel

Pre-ribosomal particles evolve in the nucleus through transient interaction with biogenesis factors, before export to the cytoplasm. Here, we report the architecture of the late pre-60S particle purified from Saccharomyces cerevisiae through Arx1, a nuclear export factor with structural homology to methionine aminopeptidases, or its binding partner Alb1. Cryo-electron microscopy reconstruction of the Arx1-particle at 11.9 Å resolution reveals regions of extra densities on the pre-60S particle attributed to associated biogenesis factors, confirming the immature state of the nascent subunit. One of these densities could be unambiguously assigned to Arx1. Immuno-electron microscopy and UV cross-linking localize Arx1 close to the ribosomal exit tunnel in direct contact with ES27, a highly dynamic eukaryotic rRNA expansion segment. The binding of Arx1 at the exit tunnel may position this export factor to prevent premature recruitment of ribosome-associated factors active during translation