Secondary caustics in close multiple lenses

We investigate the caustic structure of a lens composed by a discrete number of point-masses, having mutual distances smaller than the Einstein radius of the total mass of the system. Along with the main critical curve, it is known that the lens map is characterized by secondary critical curves producing small caustics far from the lens system. By exploiting perturbative methods, we derive the number, the position, the shape, the cusps and the area of these caustics for an arbitrary number of close multiple lenses. Very interesting geometries are created in some particular cases. Finally we review the binary lens case where our formulae assume a simple form.Comment: 9 pages with 5 figures. Accepted by A&

Signs of the cusps in binary lenses

The cusps of the caustics of any gravitational lens model can be classified into positive and negative ones. This distinction lies on the parity of the images involved in the creation/destruction of pairs occurring when a source crosses a caustic in a cusp. In this paper, we generalize the former definition of the sign of the cusps. Then we apply it to the binary lens. We demonstrate that the cusps on the axis joining the two lenses are positive while the others are negative. To achieve our objective, we combine catastrophe theory, usually employed in the derivation of the properties of caustics, with perturbative methods, in order to simplify calculations and get readable results. Extensions to multiple lenses are also considered.Comment: 18 pages, 2 figures. Accepted by Journal of Mathematical Physics. After it is published, it will be found at http://ojps.aip.org/jmp

Perturbative analysis in planetary gravitational lensing

The traditional perturbative method is applied to the case of gravitational lensing of planetary systems. A complete and detailed description of the structure of caustics for a system with an arbitrary number of planets can be obtained. I have also found precise analytical expressions for microlensing light curves perturbed by the presence of planets

Gravitational Lensing by Black Holes: a comprehensive treatment and the case of the star S2

Light rays passing very close to a black hole may experience very strong deviations. Two geometries were separately considered in the recent literature: a source behind the black hole (standard gravitational lensing); a source in front of the black hole (retro-lensing). In this paper we start from the Strong Field Limit approach to recover both situations under the same formalism, describing not only the two geometries just mentioned but also any intermediate possible configurations of the system source-lens-observer, without any small-angle limitations. This is done for any spherically symmetric black holes and for the equatorial plane of Kerr black holes. In the light of this formalism we revisit the previous literature on retro-lensing, sensibly improving the observational estimates. In particular, for the case of the star S2, we give sharp predictions for the magnitude of the relativistic images and the time of their highest brightness, which should occur at the beginning of year 2018. The observation of such images would open fascinating perspectives on the measure of the physical parameters of the central black hole, including mass, spin and distance

The complete catalogue of light curves in equal-mass binary microlensing

The light curves observed in microlensing events due to binary lenses span an extremely wide variety of forms, characterised by U-shaped caustic crossings and/or additional smoother peaks. However, all peaks of the binary-lens light curve can be traced back to features of caustics of the lens system. Moreover, all peaks can be categorised as one of only four types (cusp-grazing, cusp-crossing, fold-crossing or fold-grazing). This enables us to present the first complete map of the parameter space of the equal-mass case by identifying regions in which light curves feature the same number and nature of peaks. We find that the total number of morphologies that can be obtained is 73 out of 232 different regions. The partition of the parameter space so-obtained provides a new key to optimise modelling of observed events through a clever choice of initial conditions for fitting algorithms.Comment: 22 pages, 18 figures, accepted for publication in MNRA

O(d,d)-invariant collapse/inflation from colliding superstring waves

Generalizing previous work, we study the collision of massless superstring plane waves in D space-time dimensions within an explicitly O(D-2,D-2)-invariant set of field equations. We discuss some general properties of the solutions, showing in particular that they always lead to the formation of a singularity in the future. Using the above symmetry, we obtain entire classes of new analytic solutions with non-trivial metric, dilaton and antisymmetric field, and discuss some of their properties of specific relevance to string cosmology.Comment: 16 page

Cosmological Perturbations from a New-Physics Hypersurface

Within a broad class of inflationary models we critically analyze the way initial quantum fluctuations on a new-physics hypersurface (NPH) affect standard predictions for large-scale cosmological perturbations. We find that these so-called transplanckian effects depend crucially on the definition of the "vacuum state" in particular on which Hamiltonian is minimized on the NPH in order to select such a state. Transplanckian effects can be made much smaller than previously suggested if sufficiently "adiabatic" Hamiltonians are minimize

Caustics in gravitational lensing by mixed binary systems

We investigate binary lenses with $1/r^n$ potentials in the asymmetric case with two lenses with different indexes $n$ and $m$. These kinds of potentials have been widely used in several contexts, ranging from galaxies with halos described by different power laws to lensing by wormholes or exotic matter. In this paper, we present a complete atlas of critical curves and caustics for mixed binaries, starting from the equal-strength case, and then exploring unequal-strength systems. We also calculate the transitions between all different topology regimes. Finally we find some useful analytic approximations for the wide binary case and for the extreme unequal-strength case.Comment: 25 pages, 18 figures, in press on Universe, special issue Gravitational Lensing and Optical Geometry: A Centennial Perspectiv