Strong deflection limit of black hole gravitational lensing with arbitrary source distances

The gravitational field of supermassive black holes is able to strongly bend light rays emitted by nearby sources. When the deflection angle exceeds $\pi$, gravitational lensing can be analytically approximated by the so-called strong deflection limit. In this paper we remove the conventional assumption of sources very far from the black hole, considering the distance of the source as an additional parameter in the lensing problem to be treated exactly. We find expressions for critical curves, caustics and all lensing observables valid for any position of the source up to the horizon. After analyzing the spherically symmetric case we focus on the Kerr black hole, for which we present an analytical 3-dimensional description of the higher order caustic tubes.Comment: 20 pages, 8 figures, appendix added. In press on Physical Review

The local and global geometrical aspects of the twin paradox in static spacetimes: I. Three spherically symmetric spacetimes

We investigate local and global properties of timelike geodesics in three static spherically symmetric spacetimes. These properties are of its own mathematical relevance and provide a solution of the physical `twin paradox' problem. The latter means that we focus our studies on the search of the longest timelike geodesics between two given points. Due to problems with solving the geodesic deviation equation we restrict our investigations to radial and circular (if exist) geodesics. On these curves we find general Jacobi vector fields, determine by means of them sequences of conjugate points and with the aid of the comoving coordinate system and the spherical symmetry we determine the cut points. These notions identify segments of radial and circular gepdesics which are locally or globally of maximal length. In de Sitter spacetime all geodesics are globally maximal. In CAdS and Bertotti--Robinson spacetimes the radial geodesics which infinitely many times oscillate between antipodal points in the space contain infinite number of equally separated conjugate points and there are no other cut points. Yet in these two spacetimes each outgoing or ingoing radial geodesic which does not cross the centre is globally of maximal length. Circular geodesics exist only in CAdS spacetime and contain an infinite sequence of equally separated conjugate points. The geodesic curves which intersect the circular ones at these points may either belong to the two-surface $\theta=\pi/2$ or lie outside it.Comment: 27 pages, 0 figures, typos corrected, version published in APP

Search for new physics with neutrinos at Radioactive Ion Beam facilities

We propose applications of Radioactive Ion Beam facilities to investigate physics beyond the Standard Model. In particular, we focus on the possible measurement of coherent neutrino-nucleus scattering and on a search for sterile neutrinos, by means of a low energy beta-beam with a Lorentz boost factor $\gamma \approx 1$. In the considered setup the collected radioactive ions are sent inside a 4$\pi$ detector. For the first application we provide the number of events associated with neutrino-nucleus coherent scattering, when the detector is filled in with a noble liquid. For the sterile search we consider that the spherical detector is filled in with a liquid scintillator, and that the neutrino detection channel is inverse-beta decay. We provide the exclusion curves for the sterile neutrino mixing parameters, based upon the 3+1 formalism, depending upon the achievable ion intensity. Our results are obtained both from total rates, and including spectral information with binning in energy and in distance. The proposed experiment represents a possible alternative to clarify the current anomalies observed in neutrino experiments.Comment: 9 pages, 6 figures. v2 - added 2 figure

Delaunay Surfaces

We derive parametrizations of the Delaunay constant mean curvature surfaces of revolution that follow directly from parametrizations of the conics that generate these surfaces via the corresponding roulette. This uniform treatment exploits the natural geometry of the conic (parabolic, elliptic or hyperbolic) and leads to simple expressions for the mean and Gaussian curvatures of the surfaces as well as the construction of new surfaces.Comment: 16 pages, 11 figure