Analytic solutions of the geodesic equation in axially symmetric space-times

The complete sets of analytic solutions of the geodesic equation in Taub--NUT--(anti-)de Sitter, Kerr--(anti-)de Sitter and also in general Plebanski--Demianski space--times without acceleration are presented. The solutions are given in terms of the Kleinian sigma functions.Comment: 4 pages, 4 figures, accepted for publication in EP

Inversion of hyperelliptic integrals of arbitrary genus with application to particle motion in General Relativity

The description of many dynamical problems like the particle motion in higher dimensional spherically and axially symmetric space-times is reduced to the inversion of a holomorphic hyperelliptic integral. The result of the inversion is defined only locally, and is done using the algebro-geometric techniques of the standard Jacobi inversion problem and the foregoing restriction to the $\theta$--divisor. For a representation of the hyperelliptic functions the Klein--Weierstra{\ss} multivariable sigma function is introduced. It is shown that all parameters needed for the calculations like period matrices and Abelian images of branch points can be expressed in terms of the periods of holomorphic differentials and theta-constants. The cases of genus two and three are considered in detail. The method is exemplified by particle motion associated with a genus three hyperelliptic curve

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.

Life inside black holes

We consider test planet and photon orbits of the third kind inside a black hole, which are stable, periodic and neither come out of the black hole nor terminate at the singularity. Interiors of supermassive black holes may be inhabited by advanced civilizations living on planets with the third-kind orbits. In principle, one can get information from the interiors of black holes by observing their white hole counterparts.Comment: 4 pages, 2 figure

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

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

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

Multi-stakeholder process of co-designing small-scale fisheries policy in South Africa.

In 2005, a group of researchers, community-based organizations and lawyers got together with small-scale fishers to launch a class action law suit against the government of South Africa in its allocation system of Individual Transferable Quotas, on the ground that the system was unfair to small-scale fishing communities and threatened their right to practise their livelihoods. This effort resulted in the cabinet adoption of a new small-scale fisheries policy in 2014, with amendments being made to fisheries law (the Marine Living Resource Act 18 of 1998) to accommodate the issues and concerns of small-scale fisheries. Draft regulations and an implementation plan have recently been released, paving the way for the implementation of small-scale fisheries allocations in 2016. These legal and policy shifts are of great significance for small-scale fisheries, both in South Africa and elsewhere, and deserve careful examination. This paper discusses the processes leading to the development of a new small-scale fisheries policy and what has followed since. Specifically, the analysis focuses on a variety of collaborations between scholars from different disciplines; researchers from multiple fields; community practitioners representing diverse professional and community perspectives; and community organizations across local, state, national and international levels. The paper uses a model of change that crosses research and practitioner boundaries based on three key strategies: getting noticed; organizing at scale; and getting a seat at the negotiation table. It also considers the “transdisciplinary” process of involving all relevant actors in strategic, collective, reflection–action–reflection–action “from below”, which was crucial in the co-designing of this small-scale policy formulation in South Africa