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

Neutrino Oscillations in Caianiello's Quantum Geometry Model

Neutrino flavor oscillations are analyzed in the framework of Quantum Geometry model proposed by Caianiello. In particular, we analyze the consequences of the model for accelerated neutrino particles which experience an effective Schwarzschild geometry modified by the existence of an upper limit on the acceleration, which implies a violation of the equivalence principle. We find a shift of quantum mechanical phase of neutrino oscillations, which depends on the energy of neutrinos as E^3. Implications on atmospheric and solar neutrinos are discussed.Comment: 11 page

Light's Bending Angle due to Black Holes: From the Photon Sphere to Infinity

The bending angle of light is a central quantity in the theory of gravitational lensing. We develop an analytical perturbation framework for calculating the bending angle of light rays lensed by a Schwarzschild black hole. Using a perturbation parameter given in terms of the gravitational radius of the black hole and the light ray's impact parameter, we determine an invariant series for the strong-deflection bending angle that extends beyond the standard logarithmic deflection term used in the literature. In the process, we discovered an improvement to the standard logarithmic deflection term. Our perturbation framework is also used to derive as a consistency check, the recently found weak deflection bending angle series. We also reformulate the latter series in terms of a more natural invariant perturbation parameter, one that smoothly transitions between the weak and strong deflection series. We then compare our invariant strong deflection bending-angle series with the numerically integrated exact formal bending angle expression, and find less than 1% discrepancy for light rays as far out as twice the critical impact parameter. The paper concludes by showing that the strong and weak deflection bending angle series together provide an approximation that is within 1% of the exact bending angle value for light rays traversing anywhere between the photon sphere and infinity.Comment: 22 pages, 5 figure

Quasi-Equatorial Gravitational Lensing by Spinning Black Holes in the Strong Field Limit

Spherically symmetric black holes produce, by strong field lensing, two infinite series of relativistic images, formed by light rays winding around the black hole at distances comparable to the gravitational radius. In this paper, we address the relevance of the black hole spin for the strong field lensing phenomenology, focusing on trajectories close to the equatorial plane for simplicity. In this approximation, we derive a two-dimensional lens equation and formulae for the position and the magnification of the relativistic images in the strong field limit. The most outstanding effect is the generation of a non trivial caustic structure. Caustics drift away from the optical axis and acquire finite extension. For a high enough black hole spin, depending on the source extension, we can practically observe only one image rather than two infinite series of relativistic images. In this regime, additional non equatorial images may play an important role in the phenomenology.Comment: 13 pages, 9 figures. Improved version with detailed physical discussio

The weakly perturbed Schwarzschild lens in the strong deflection limit

We investigate the strong deflection limit of gravitational lensing by a Schwarzschild black hole embedded in an external gravitational field. The study of this model, analogous to the Chang & Refsdal lens in the weak deflection limit, is important to evaluate the gravitational perturbations on the relativistic images that appear in proximity of supermassive black holes hosted in galactic centers. By a simple dimensional argument, we prove that the tidal effect on the light ray propagation mainly occurs in the weak field region far away from the black hole and that the external perturbation can be treated as a weak field quadrupole term. We provide a description of relativistic critical curves and caustics and discuss the inversion of the lens mapping. Relativistic caustics are shifted and acquire a finite diamond shape. Sources inside the caustics produce four sequences of relativistic images. On the other hand, retro-lensing caustics are only shifted while remaining point-like to the lowest order.Comment: 12 pages, 1 figure

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

A comparison of approximate gravitational lens equations and a proposal for an improved new one

Keeping the exact general relativistic treatment of light bending as a reference, we compare the accuracy of commonly used approximate lens equations. We conclude that the best approximate lens equation is the Ohanian lens equation, for which we present a new expression in terms of distances between observer, lens and source planes. We also examine a realistic gravitational lensing case, showing that the precision of the Ohanian lens equation might be required for a reliable treatment of gravitational lensing and a correct extraction of the full information about gravitational physics.Comment: 11 pages, 6 figures, to appear 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

Prediction in forensic science: a critical examination of common understandings

In this commentary, we argue that the term 'prediction' is overly used when in fact, referring to foundational writings of de Finetti, the correspondent term should be inference. In particular, we intend (i) to summarize and clarify relevant subject matter on prediction from established statistical theory, and (ii) point out the logic of this understanding with respect practical uses of the term prediction. Written from an interdisciplinary perspective, associating statistics and forensic science as an example, this discussion also connects to related fields such as medical diagnosis and other areas of application where reasoning based on scientific results is practiced in societal relevant contexts. This includes forensic psychology that uses prediction as part of its vocabulary when dealing with matters that arise in the course of legal proceedings

La naturaleza decisoria de las conclusiones de los expertos en ciencia forense (The decisionalization of individualization)

En la ciencia forense y ramas de la ciencia adyacentes, tanto investigadores del ámbito académico como quienes las practican continúan divergiendo en la percepción y comprensión del término “individualización”, es decir, la defensa de la tesis de que es posible reducir un conjunto de potenciales donantes de un vestigio forense a una única fuente. En concreto, se ha puesto de manifiesto que recientes cambios que entienden la práctica de la individualización como una decisión no son más que un mero cambio de etiqueta [1], dejando los cambios fundamentales en el orden del pensar y del entender aún pendientes. Es más, asociaciones profesionales y expertos huyen de adherirse a la noción de decisión tal y como la define la teoría formal de la decisión en la que la individualización puede contextualizarse, principalmente por las dificultades para tratar sobre las medidas de deseabilidad o no de las consecuencias de las decisiones (por ejemplo, utilizando las funciones de utilidad). Apoyándose en investigaciones existentes en esta área, este artículo presenta y discute sobre conceptos fundamentales de utilidades y costes, con particular referencia a su aplicación a la individualización forense. El artículo subraya que una adecuada comprensión de las herramientas de la decisión no solo reduce el número de asignaciones individuales que la aplicación de la teoría de la decisión requiere, sino que también muestra cómo esas asignaciones pueden relacionarse significativamente con las propiedades constituyentes del problema de la decisión en el mundo real al que se aplica la teoría. Se argumenta que la “decisionalización” de la individualización requiere esa percepción fundamental para iniciar cambios en las comprensiones subyacentes de esos campos, no meramente en el ámbito de sus etiquetas