Strong field limit analysis of gravitational retro-lensing

We present a complete treatment in the strong field limit of gravitational retro-lensing by a static spherically symmetric compact object having a photon sphere. The results are compared with those corresponding to ordinary lensing in similar strong field situations. As examples of application of the formalism, a supermassive black hole at the galactic center and a stellar mass black hole in the galactic halo are studied as retro-lenses, in both cases using the Schwarzschild and Reissner-Nordstrom geometries.Comment: 11 pages, 1 figure; v2: minor changes. Accepted for publication in Physical Review

Strong Gravitational Lensing by Sgr A*

In recent years, there has been increasing recognition of the potential of the galactic center as a probe of general relativity in the strong field. There is almost certainly a black hole at Sgr A* in the galactic center, and this would allow us the opportunity to probe dynamics near the exterior of the black hole. In the last decade, there has been research into extreme gravitational lensing in the galactic center. Unlike in most applications of gravitational lensing, where the bending angle is of the order of several arc seconds, very large bending angles are possible for light that closely approaches a black hole. Photons may even loop multiple times around a black hole before reaching the observer. There have been many proposals to use light's close approach to the black hole as a probe of the black hole metric. Of particular interest is the property of light lensed by the S stars orbiting in the galactic center. This paper will review some of the attempts made to study extreme lensing as well as extend the analysis of lensing by S stars. In particular, we are interested in the effect of a Reissner-Nordstrom like 1/r^2 term in the metric and how this would affect the properties of relativistic images.Comment: 13 pages, 9 figures. Submitted as invited review article for the GR19 issue of CQ

Gravitational lensing of transient neutrino sources by black holes

In this work we study gravitational lensing of neutrinos by Schwarzschild black holes. In particular, we analyze the case of a neutrino transient source associated with a gamma-ray burst lensed by a supermassive black hole located at the center of an interposed galaxy. We show that the primary and secondary images have an angular separation beyond the resolution of forthcoming km-scale detectors, but the signals from each image have time delays between them that in most cases are longer than the typical duration of the intrinsic events. In this way, the signal from different images can be detected as separate events coming from the very same location in the sky. This would render an event that otherwise might have had a low signal-to-noise ratio a clear detection, since the probability of a repetition of a signal from the same direction is negligible. The relativistic images are so faint and proximate that are beyond the sensitivity and resolution of the next-generation instruments.Comment: 9 pages; v2: improved version, new references added. Accepted for publication in Physics Letters

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

Gravitational lensing in the strong field limit

We provide an analytic method to discriminate among different types of black holes on the ground of their strong field gravitational lensing properties. We expand the deflection angle of the photon in the neighbourhood of complete capture, defining a strong field limit, in opposition to the standard weak field limit. This expansion is worked out for a completely generic spherically symmetric spacetime, without any reference to the field equations and just assuming that the light ray follows the geodesics equation. We prove that the deflection angle always diverges logarithmically when the minimum impact parameter is reached. We apply this general formalism to Schwarzschild, Reissner-Nordstrom and Janis-Newman-Winicour black holes. We then compare the coefficients characterizing these metrics and find that different collapsed objects are characterized by different strong field limits. The strong field limit coefficients are directly connected to the observables, such as the position and the magnification of the relativistic images. As a concrete example, we consider the black hole at the centre of our galaxy and estimate the optical resolution needed to investigate its strong field behaviour through its relativistic images.Comment: 10 pages, 5 figures, in press on Physical Review

Status of Salerno Laboratory (Measurements in Nuclear Emulsion)

A report on the analysis work in the Salerno Emulsion Laboratory is presented. It is related to the search for nu_mu->nu_tau oscillations in CHORUS experiment, the calibrations in the WANF (West Area Neutrino Facility) at Cern and tests and preparation for new experiments.Comment: Proc. The First International Workshop of Nuclear Emulsion Techniques (12-24 June 1998, Nagoya, Japan), 15 pages, 11 figure

Efficient Thermal Electric Skipping Strategy Applied to the Control of Series/Parallel Hybrid Powertrain

The optimal control of hybrid powertrains represents one of the most challenging tasks for the compliance with the legislation concerning CO2 and pollutant emission of vehicles. Most common off-line optimization strategies (Pontryagin minimum principle-PMP-or dynamic programming) allow to identify the optimal control along a predefined driving mission at the expense of a quite relevant computational effort. On-line strategies, suitable for on-vehicle implementation, involve a certain performance degradation depending on their degree of simplification and computational effort. In this work, a simplified control strategy is presented, where the conventional power-split logics, typical of the above-mentioned strategies, is here replaced with an alternative utilization of the thermal and electric units for the vehicle driving (Efficient Thermal Electric Skipping Strategy-ETESS). The choice between the units is realized at each time and is based on the comparison between the effective fuel rate of the thermal engine and an equivalent fuel rate related to the electrical power consumption. The equivalent fuel rate in a pure electric driving is associated to a combination of brake specific fuel consumption of the thermal engine, and electro-mechanical efficiencies along the driveline. The ETESS is applied for the simulation of segment C hybrid vehicle, equipped with a thermal engine and two electric units (motor and generator). The methodology is tested along regulatory driving cycles (WLTP, Artemis) and RDE, with different powertrain variants. Numerical results underline that the proposed approach performs very close to most common control strategies (consumed fuel per kilometer higher than PMP of about 1% on average). The main advantage is a reduced computational effort (decrease of 99% on average). The ETESS is straightforwardly adapted for an on-line implementation, through the introduction of an adaptative factor, preserving the computational effort and the fuel economy

Reissner-Nordstrom black hole lensing

In this paper we study the strong gravitational lensing scenario where the lens is a Reissner-Nordstrom black hole. We obtain the basic equations and show that, as in the case of Schwarzschild black hole, besides the primary and secondary images, two infinite sets of relativistic images are formed. We find analytical expressions for the positions and amplifications of the relativistic images. The formalism is applied to the case of a low-mass black hole placed at the galactic halo.Comment: 16 pages, 5 figure