Gravitational Lens Effect Research Articles

Gravitational lens effect of a holonomy corrected Schwarzschild black hole

Gravitational lens effect of a holonomy corrected Schwarzschild black hole

Comparison of Different Types of Black Holes

With the deeper exploration on black hole, more and more categories of black holes are defined by astronomers and physicists. The article will discuss the differences in detection and process of accretion between the binary black holes and isolated black holes through analysing previous researches on black holes. To search for binary black holes, whose companion may be luminous, classical methods include spectrum test and calculation of the operation of binary star system are applied. On the other hand, the state-or-art facilities HST are used to detect them based on gravitational lens effect. These two different sorts of black holes also have their unique process of accretion. The binary black holes absorb particles from the stellar wind which is given out by their companion, forming two “minidisk”. The process is accompanied with strong emission of X-ray. Meanwhile, the accretion of isolated black hole forms only one ring of gas. The accretion flow is mostly weak and radioactively inefficient. The reason for these differences can be their separate optical features and relationships with environment. It is aimed at distinguishing the two kinds of black holes with different framework, making them easier to identify only with optical evidence or data on radioactive emission. Therefore, it’s easy to tell the infer structure from evidence that astronomers can comparatively easier obtain about black holes, which is beneficial for further studies about black holes internal structure details. These results shed light on guiding further exploration of black holes.

Local and Global Properties of the Gravitational Lens Effect with Special Consideration of the Gravitational Lens Effect with Star Perturbation.

Since the late 1970s, gravitational lensing became an important tool in astrophysics, taking advantage of the lens-like bending of light by masses such as planets, stars, galaxies, or clusters of them to determine their properties or even their existence. At that time and later in the 80s, the group at the Hamburg observatory around Sjur Refsdal developed many techniques that are still in use to understand and apply the effect. Although the effect is a consequence of Einstein's general theory of relativity, the equations used to describe the effects of masses on light rays are relatively simple. However, in order to answer questions about what a light source looks like through a special lens, or whether there might be multiple images of a light source, the math got quite complicated and the problems were largely solved numerically.In this article we show, for an important special case of a star in a galaxy as a lens, that the problems of differential geometry that arise can be treated algebraically by a computer algebra system such as Maple and lead to elegant solutions that are generally applicable to mappings from the plane onto the plane.

Gravitational lens effect revisited through membrane waves

By means of experiments and curved manifold simulations, we show that wave propagation past a topological deviation on a two-dimensional flat fabric membrane is analogous to gravitational lensing. Using an ultrafast camera, we track a membrane plane wave as it crosses a local warped depression. Finite difference simulation, based on the scalar wave equation in a Schwarzschild metric, fully describes the experimental wavefront shape. Comparison between the theoretical and experimental deviation of wave geodesics from straight lines shows that (i) the nonlinear behavior of fabrics due to stretching induces second order effects only and (ii) the experimental depression is closely approximated by the Schwarzschild metric of a gravity well. The experiment demonstrates, in a simple way, how wave propagation is influenced by the topology of the transmission medium.

Topological deviation of membrane waves as a model of gravitational lens effect

Elastic membranes are often used as didactic demonstration of gravitation from the general relativity perspective. Indeed, trajectories of rolling spheres such as billiard balls influence each other through the deformation their mass print within the membrane tissue as would the space-time curvature of gravity. The analogy is pushed here using membrane waves. Indeed, rules of topology apply to masses and waves. We show through experiments and curved manifold simulations that wave propagation due to topological deviation of a two-dimensional flat fabric membrane, justifies classical analogy with gravitational lenses. This allows revisiting through membrane waves, the famous 1919 Eddington experiment that demonstrated light deviations of stars in the vicinity of the sun. It is our hope that the experiment described here will provide new insight for the testing of geometry effects on wave propagation. Also, inspired by acoustic metamaterials, it is our hope to use a more correctly constructed membrane to observe quantified exchanges of geometric waves with their elementary mesh.

Extended lens reconstructions with grale: exploiting time-domain, substructural, and weak lensing information

ABSTRACT The information about the mass density of galaxy clusters provided by the gravitational lens effect has inspired many inversion techniques. In this article, updates to the previously introduced method in grale are described, and explored in a number of examples. The first looks into a different way of incorporating time delay information, not requiring the unknown source position. It is found that this avoids a possible bias that leads to ‘overfocusing’ the images, i.e. providing source position estimates that lie in a considerably smaller region than the true positions. The second is inspired by previous reconstructions of the cluster of galaxies MACS J1149.6+2223, where a multiply imaged background galaxy contained a supernova, SN Refsdal, of which four additional images were produced by the presence of a smaller cluster galaxy. The inversion for the cluster as a whole was not able to recover sufficient detail interior to this quad. We show how constraints on such different scales, from the entire cluster to a single member galaxy, can now be used, allowing such small-scale substructures to be resolved. Finally, the addition of weak lensing information to this method is investigated. While this clearly helps recover the environment around the strong lensing region, the mass sheet degeneracy may make a full strong and weak inversion difficult, depending on the quality of the ellipticity information at hand. We encounter ring-like structure at the boundary of the two regimes, argued to be the result of combining strong and weak lensing constraints, possibly affected by degeneracies.

An optical n-body gravitational lens analogy

Raised menisci around small discs positioned to pull up a water-air interface provide a highly controllable experimental setup capable of reproducing much of the rich phenomenology of gravitational lensing (or microlensing) by n-body clusters. Results are shown for single, binary, and triple mass systems. The scheme represents a versatile testbench for the (astro)physics of general relativity's gravitational lens effects, including high multiplicity imaging of extended sources.

Dark Matter Garden: A case study in algorithmic modelling and digital fabrication of complex steel structures

This paper is focusing on the application of algorithmic modelling techniques to represent, design and fabricate gravitational lens effects (as described by the astrophysical theory of the ‘Dark Matter’) in form of a garden pavilion for the Royal Horticultural Society's, Chelsea Flower Show. In addition, this research-led project is exploring the challenges occurring in the use of three-dimensional CNC bending technologies. This is a research by design project and its method is based on a design framework, which incorporates a generative algorithm linked to feedback loops related to parameters such as laws of gravity, plot dimensions, materiality, positioning of the plants, construction and fabrication, requirements and cost as well as the overall aesthetics. Its findings are highlighting accomplishments and failures of a file to factory design and fabrication process, which incorporates algorithmic modelling and digital manufacturing techniques in a collaborative environment. The ‘Dark Matter Garden’ installation was awarded the gold medal for ‘Best Fresh Garden’ by the Royal Horticultural Society in 2015.

Constraints on Dark Energy Models from Galaxy Clusters and Gravitational Lensing Data

The Sunyaev–Zel’dovich (SZ) effect is a global distortion of the Cosmic Microwave Background (CMB) spectrum as a result of its interaction with a hot electron plasma in the intracluster medium of large structures gravitationally viralized such as galaxy clusters (GC). Furthermore, this hot gas of electrons emits X-rays due to its fall in the gravitational potential well of the GC. The analysis of SZ and X-ray data provides a method for calculating distances to GC at high redshifts. On the other hand, many galaxies and GC produce a Strong Gravitational Lens (SGL) effect, which has become a useful astrophysical tool for cosmology. We use these cosmological tests in addition to more traditional ones to constrain some alternative dark energy (DE) models, including the study of the history of cosmological expansion through the cosmographic parameters. Using Akaike and Bayesian Information Criterion, we find that the w C D M and Λ C D M models are the most favoured by the observational data. In addition, we found at low redshift a peculiar behavior of slowdown of the universe, which occurs in dynamical DE models when we use data from GC.

Weak gravitational lensing of quantum perturbed lukewarm black holes and cosmological constant effect

The aim of the paper is to study weak gravitational lensing of quantum (perturbed) and classical lukewarm black holes (QLBHs and CLBHs respectively) in the presence of cosmological parameter Λ. We apply a numerical method to evaluate the deflection angle of bending light rays, image locations θ of sample source and corresponding magnifications μ. There are no obtained real values for Einstein ring locations for CLBHs but we calculate them for QLBHs. As an experimental test of our calculations, we choose mass M of 60 types of the most massive observed galactic black holes acting as a gravitational lens and study quantum matter field effects on the angle of bending light rays in the presence of cosmological constant effects. We calculate locations of non-relativistic images and corresponding magnifications. Numerical diagrams show that the quantum matter effects cause absolute values of the quantum deflection angle to be reduced with respect to the classical ones. The sign of the quantum deflection angle is changed with respect to the classical values in the presence of the cosmological constant. This means dominance of the anti-gravity counterpart of the cosmological horizon on the angle of bending light rays with respect to absorbing effects of 60 local types of the most massive observed black holes. Variations of the image positions and magnifications are negligible when increasing dimensionless cosmological constant . The deflection angle takes positive (negative) values for CLBHs (QLBHs) and they decrease very fast (slowly) by increasing the closest distance x0 of bending light ray and/or dimensionless cosmological parameter for sample giant black holes with .

Hesperides: Solar/nuclear missions to the Sun׳s inner gravity focus

The Sun׳s gravity focus at >550AU is of interest to astrophysicists including SETI scientists, researchers seeking to image extra-solar planets and others. One method for an extra-solar probe to reach the Sun׳s inner gravity focus within a human working lifetime (less than 50 years) is to combine solar and nuclear propulsion techniques. Here, we present a non-optimized probe concept including state-of-the-art solar-sail, radioisotope-electric propulsion and giant-planet gravity assists. Application of radioisotope propulsion allows some cross range capability during and after the powered and cruise phases of the flight to >600AU. Such a capability is likely necessary to fully utilize the solar gravitational lens effect for SETI and astrophysical observations.

An Eccentric Derivation of the Gravitational-Lens Effect

The gravitational-lens effect is interpreted in the framework of the Newtonian mechanics. Regarding the photon of energy hv as a corpuscle with a tiny mass of mγ=hv/c2. We calculate it's path bended by the gravitational force near the surface of the sun. Effects of dark matter have also been evaluated.

An Analytical Approximation of the Luminosity Distance in Flat Cosmologies with a Cosmological Constant

We present an analytical approximation formula for the luminosity distance in spatially flat cosmologies with dust and a cosmological constant. Apart from the overall factor, the effect of non-zero cosmological constant in our formula is written simply in terms of a rational function. We also show the approximate formulae for the Dyer-Roeder distance (empty beam case) and the generalized angular diameter distance from redshift $z_1$ to $z_2$, which are particularly useful in analyzing the gravitational lens effects. Our formulae are widely applicable over the range of the density parameter and the redshift with sufficiently small uncertainties. In particular, in the range of density parameter $0.3 \leq \Omega_{\rm m} \leq 1$ and redshift $0.03 \leq z \leq 1000$, the relative error for the luminosity distance by our formula is always smaller than that of the recent work by Wickramasinghe and Ukwatta (2010). Hence, we hope that our formulae will be an efficient and useful tool for exploring various problems in observational cosmology.

Observations in a locally inhomogeneous Universe and Dark Energy State Equation

Determining the redshift of astronomical sources is fundamental for cosmological studies, since it allows deriving distances to the observer. However, the distance-redshift relationship commonly used is obtained from the isotropic, homogeneous Friedmann-Lemaitre-Robertson-Walker (FLRW) metric. By fitting this distance-redshift relations to Supernovae Ia data, used by many authors as standard candles for distance measurements, it was shown that the expansion of the universe is accelerating, since the addittion of equations of state in the cosmological model was required. Whether this dark energy is a cosmological constant or a quintessence is still to be determined, and is the objective of some current and future dark energy studies.However, the Universe is not homogeneuos. The gravitational lens effect changes the luminosity of distant sources, and it may also change significantly the angular diameter distance, thus modifying the luminosity distance, changing the distance-redshift relation with respect to that of an homogeneous universe. This effect can be considered an additional source of dispersion of the data, affecting the determination of the dark energy equation of state.We are developing a test for studying departures from the FLRW distance-redshift relation, and its impact on the determination of the dark energy equation of state.

Perturbative Approach to the Gravitational Lensing by a Non-Spherically Distorted Compact Object

We investigate the gravitational lens effect caused by a non-spherically distorted compact object. The non-spherical property of the gravitational potential is modeled by a quadrupole moment. Under the assumption that the quadrupole contribution is small, we solve perturbatively the lens equation and obtain the image positions and the amplification factors. We show that the separation angle of two major images is only slightly changed by the existence of the quadrupole contribution, whereas the difference of the amplification factors may be significantly modified. Our results indicate that even a tiny non-spherical distortion of the lens potential may cause significant amount of flux anomalies in the lensed images.

Interstellar radio links enhanced by exploiting the Sun as a Gravitational Lens

The gravitational lens of the Sun is an astrophysical phenomenon predicted by Einstein’s general theory of relativity. It implies that if we can send a probe along any radial direction away from the Sun up to the minimal distance of 550 AU and beyond, the Sun’s mass will act as a huge magnifying lens, letting us “see” detailed radio maps of whatever may lie on the other side of the Sun even at very large distances. The recent book by this author (Claudio Maccone, Deep Space Flight and Communications, 414 pages, Praxis-Springer, 2009) describes such future FOCAL space missions to 550 AU and beyond. In this paper, however, we want to study another possibility yet: how to enable the future interstellar radio links between the solar system and any future interstellar probe by utilizing the gravitational lens of the Sun as a huge antenna. In particular, we compare the bit error rate (BER) across interstellar distances with and without using the gravitational lens effect of the Sun. The conclusion is that only when we will exploit the Sun as a gravitational lens we will be able to communicate with our own probes (or with nearby Aliens) across the distances of even the nearest stars to us in the Galaxy and that at a reasonable bit error rate. Furthermore, we study the radio bridge between the Sun and any other Star that is made up by the two gravitational lenses of both the Sun and that Star. The alignment for this radio bridge to work is very strict, but the power saving is enormous, due to the huge contributions of the two stars’ lenses to the overall antenna gain of the system. For instance, we study in detail: 1) The Sun–Alpha Cen A radio bridge. 2) The Sun–Barnard’s star radio bridge. 3) The Sun–Sirius A radio bridge. 4) The radio bridge between the Sun and any Sun-like star located in the galactic bulge. 5) The radio bridge between the Sun and any Sun-like star located inside the Andromeda galaxy (M 31). The conclusion is that a radio interstellar communications network can indeed be built if the gravitational lenses of all stars involved are exploited. Then, the new question arises: has any advanced civilization already built such a radio telecommunication network? If so, our current and future SETI searches should be tuned-up to match with this newly realized possibility.

Cosmic chiral vortices

The review is devoted to cosmic chiral vortices (strings) and their possible role in the evolution of the early Universe. An exact cylindrically-symmetric solution to Einstein equations was obtained within the SU(2) sigma model for a configuration with a topological charge of the degree type. The linearized stability of the solution with respect to radial perturbations is proven by Lyapunov’s direct method. The metric found corresponds to the conical type with an angular deficiency proportional to the topological charge or the linear mass density of the vortex. The ray deflection angle close to the angular deficiency (the gravitational lens effect) was determined by direct integration of geodesic equations for the light ray orthogonal to the vortex. A gauge generalization of the model was considered involving the axially symmetric Yang-Mills field. In the approximation of the large topological charge, a solution with proper longitudinal magnetic field was obtained and the effect of a decrease in the vortex energy was found. The effect of closing the string was also considered in the approximation of the large closure radius. To this end, the toroidal moment of a closed string was calculated and an energy correction caused by the Skyrme term.

Neutrino Lensing

Due to the intrinsic properties of neutrinos, the gravitational lens effect for a neutrino should be more colorful and meaningful than the normal lens effect of a photon. Other than the experiments operated at terrestrial laboratory, in principle, we can propose a completely new astrophysical method to determine not only the nature of the gravity of lens objects but also the mixing parameters of neutrinos by analyzing neutrino trajectories near the central objects. However, the angular, energy and time resolution of the neutrino telescopes are still comparatively poor, so we just concentrate on the two classical tests of general relativity, i.e. the angular deflection and the time delay of the neutrino by a lens object as a preparative work in this paper. In addition, some simple properties of neutrino lensing are investigated.

Strong gravitational lensing: relativity in action

AbstractDeflection of light by gravity was predicted by Einstein's Theory of General Relativity and observationally confirmed in 1919. In the following decades, various aspects of the gravitational lens effect were explored theoretically, among them measuring the Hubble constant from multiple images of a background source, making use of the magnifying effect as a gravitational telescope, or the possibility of a “relativistic eclipse” as a perfect test of GR. Only in 1979, gravitational lensing became an observational science when the first doubly imaged quasar was discovered. Today lensing is a booming part of astrophysics and cosmology. A whole suite of strong lensing phenomena have been investigated: multiple quasars, giant luminous arcs, Einstein rings, quasar microlensing, and galactic microlensing. The most recent lensing application is the detection of extrasolar planets. Lensing has contributed significant new results in areas as different as the cosmological distance scale, mass determination of galaxy clusters, physics of quasars, searches for dark matter in galaxy halos, structure of the Milky Way, stellar atmospheres and exoplanets. A guided tour through some of these applications will illustrate how gravitational lensing has established itself as a very useful universal astrophysical tool.

High‐Energy Properties of PKS 1830−211

We report on an analysis of X- and $\gamma$-ray observations of PKS 1830-211, based on the long-term campaigns carried out by \emph{INTEGRAL} and COMPTEL. The \emph{INTEGRAL} data currently available present a $33\sigma$ significance detection in the 20-100 keV band, while the COMPTEL 6-years data provide a $5.2\sigma$ significance detection in the 1-3 MeV energy band. At hard X-rays, \emph{INTEGRAL} and supplementary \emph{SWIFT} observations show flux variability on timescales of months. At $\gamma$-rays, the source shows persistent emission over years. The hard X-ray spectrum is well represented by a power-law model, with $\Gamma \sim 1.3$ in the 20-250 keV band. This photon index is well consistent with the previous report of $\Gamma \sim 1.3$ obtained at $E > 3.5$ keV from the best fit of \emph{XMM-Newton} data with a broken power law model. The joint \emph{XMM-Newton}/\emph{INTEGRAL} spectrum presented here is then fit with a broken power-law model and the parameters are refined compared to the previous. The results show the photon index changes from $\sim 1.0$ to $\sim 1.3$ at a break energy $\sim 4$ keV. At MeV energies, the spectrum softens to $\Gamma \sim 2.2$. These results, together with the EGRET measurement at $E \ge 100$ MeV, constitute a broad-band spectrum containing the peak of the power output at MeV energies, similar to most high-luminosity $\gamma$-ray blazars. The measured spectral characterstics are then discussed in the framework of the gravitational lens effects.