Lensing Effect Research Articles

Searching for Dark Matter Based on Gravitational Lensing

Gravitational lensing is a powerful astronomical tool in which scholars can accurately predict the distribution of dark matter in massive objects by observing the bending effects of light in the gravitational fields of huge objects (e.g., galaxies or galaxy clusters). Since dark matter does not emit directly, or is strongly interacts with ordinary matter, gravitational lensing gives us a unique view of observing and measuring dark matter. This study introduces some principles of gravitational lensing effect to provide favorable evidence in the study of dark matter and other celestial bodies (including an engineering study in the focal region of solar gravitational lensing (SGL) and other experiments). This research will see how the properties of the clear and focused gravitational lens are applied to celestial observations, and how they are captured by the detector. Strong gravitational lensing can better show distant galaxies (including high redshift) around the dark matter distribution, and through the several basic quantities in gravitational lens analytical and numerical calculation and analysis, to simulate the center of the supermassive black hole, and gravitational lensing image and model of dark matter mass can be detected and dark matter has the key evidences of the interaction. It reveals the intrinsic and distribution of dark matter, thus driving the understanding of the universe’s evolution and its fundamental components. Therefore, gravitational lensing has an irreplaceable value and a far-reaching influence in exploring the unsolved mystery of dark matter.

Analogy of space-time as an elastic medium - Estimation of a creep coefficient of space from space data via the MOND theory and the gravitational lensing effect - the ball cluster and via time data from the GPS effect- comparison, discussion and implication of the results for dark matter and Einstein's field equation

Analogy of space-time as an elastic medium - Estimation of a creep coefficient of space from space data via the MOND theory and the gravitational lensing effect - the ball cluster and via time data from the GPS effect- comparison, discussion and implication of the results for dark matter and Einstein's field equation

Cyclotron resonance imaging at cryogenic temperatures enabled by electric field modification in a microwave cavity

Abstract Cyclotron resonance (CR) is a standard but emerging technique for investigating carrier properties of semiconductors. We have succeeded in CR measurements by employing a microwave cavity designed for electron paramagnetic resonance (EPR). Here, we demonstrate CR imaging to visualize the spatial distribution of carriers at cryogenic temperatures for the first time. To realize CR imaging, it is necessary to account for the electric field modification in the microwave cavity of a cylindrical TM110 mode, which is designed for EPR imaging and is inherently unsuitable for CR measurements. CR detection requires the oscillating electric field perpendicular to the external static magnetic field (B0) at the sample position, which is not designed for the unloaded cavity. It has been challenging to verify the electric field distribution inside the cavity experimentally, but we show that the observation of the CR signals provides evidence of modification in the electric field. Analysis of the electromagnetic field explains the results, revealing a field distribution whose strength and direction are perturbed due to the lensing effect by the inserted dielectric materials.

Gravitational wave luminosity distance-weighted anisotropies

Measurements of the luminosity distance of propagating gravitational waves can provide invaluable information on the geometry and content of our Universe. Due to the clustering of cosmic structures, in realistic situations we need to average the luminosity distance of events coming from patches inside a volume. In this work we evaluate, in a gauge-invariant and fully-relativistic treatment, the impact of cosmological perturbations on such averaging process. We find that clustering, lensing and peculiar velocity effects impact estimates for future detectors such as Einstein Telescope, Cosmic Explorer, the Big Bang Observer and DECIGO. The signal-to-noise ratio of the angular power spectrum of the average luminosity distance over all the redshift bins is 17 in the case of binary black holes detected by Einstein Telescope and Cosmic Explorer. We also provide fitting formulas for the corrections to the average luminosity distance due to general relativistic effects.

The lensing effect of quantum-corrected black hole and parameter constraints from EHT observations

The quantum-corrected black hole model demonstrates significant potential in the study of gravitational lensing effects. By incorporating quantum effects, this model addresses the singularity problem in classical black holes. In this paper, we investigate the impact of the quantum correction parameter on the lensing effect based on the quantum-corrected black hole model. Using the black holes M87∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M87^*$$\\end{document} and SgrA∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Sgr A^*$$\\end{document} as our subjects, we explore the influence of the quantum correction parameter on angular position, Einstein ring, and time delay. Additionally, we use data from the Event Horizon Telescope observations of black hole shadows to constrain the quantum correction parameter. Our results indicate that the quantum correction parameter significantly affects the lensing coefficients a¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{a}$$\\end{document} and b¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{b}$$\\end{document}, as well as the Einstein ring. The position θ∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{\\infty }$$\\end{document} and brightness ratio S of the relativistic image exhibit significant changes,with deviations on the order of magnitude of ∼1μas\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 1\\,\\upmu \\! \ extrm{as}$$\\end{document} and ∼0.01μas\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 0.01\\,\\upmu \\! \ extrm{as}$$\\end{document}, respectively. The impact of the quantum correction parameter on the time delay ΔT21\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta T_{21}$$\\end{document} is particularly significant in the M87∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M87^*$$\\end{document} black hole, with deviations reaching up to several tens of hours. Using observational data from the Event Horizon Telescope(EHT) of black hole shadows to constrain the quantum correction parameter, the constraint range under the M87∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M87^*$$\\end{document} black hole is 0≤αM2≤1.4087\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0\\le \\frac{\\alpha }{M^2}\\le 1.4087$$\\end{document} and the constraint range under the SgrA∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Sgr A^*$$\\end{document} black hole is 0.9713≤αM2≤1.6715\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.9713\\le \\frac{\\alpha }{M^2}\\le 1.6715$$\\end{document}. Although the current resolution of the EHT limits the observation of subtle differences, future high-resolution telescopes are expected to further distinguish between the quantum-corrected black hole and the Schwarzschild black hole, providing new avenues for exploring quantum gravitational effects.

Gravitational lensing and shadow by a Schwarzschild-like black hole in metric-affine bumblebee gravity

In this paper, we investigate the gravitational lensing effect and the shadow around a Schwarzschild-like black hole in metric-affine bumblebee gravity, which leads to the Lorentz symmetry breaking. We first present a generalized formalism for calculating higher-order corrections to light weak bending angle in a static, spherically symmetric and not asymptotically flat spacetime, and then applying this general formalism to the metric-affine bumblebee gravity. Moreover, we derive the light deflection angle and the size of the Einstein ring within the weak field in this scenario. In addition, we analyze the black hole shadow in this theory framework. By using observational data from the Einstein’s ring of the galaxy ESO325-G004 and the black hole shadow of the M87\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{M}87$$\\end{document} galaxy, we estimate the upper bounds of the Lorentz symmetry breaking coefficient ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell $$\\end{document}, respectively.

Bright compact ultrabroadband source by orthogonal laser-sustained plasma

Laser-sustained plasma (LSP) source featuring high brightness and broadband spectral coverage is found to be powerful in various fields of scientific and industrial applications. However, the fundamental limit of low conversion efficiency constrains the system compactness and widespread applications of such broadband light sources. In this paper, we propose an innovative orthogonal LSP to break through the conversion efficiency limitation. Driven by the elevated conversion efficiency from absorbed laser power to ultraviolet (UV) emission, a compact broadband source (250–1650 nm) with UV spectral radiance exceeding 210 mW/(mm2⋅sr⋅nm)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${mW}/({{mm}}^{2}\\,\\cdot\\, {sr}\\,\\cdot\\, {nm})$$\\end{document} is achieved with >100 W pump laser. With the plot of a two-dimensional refractive index model, we report an important conceptual advance that the orthogonal design eliminates the influence of the negative lensing effect on laser power density. Experimental results unambiguously demonstrate that we achieve a bright compact UV-VIS-NIR source with negligible thermal loss and the highest conversion efficiency to our knowledge. Significant enhancement of 4 dB contrast-to-noise ratio (CNR) in spectral single-pixel imaging has been demonstrated using the proposed ultrabroadband source. By establishing the quantitative link between pumping optics design and plasma absorption, this work presents a compact broadband source that combines superior conversion efficiency and unprecedented brightness, which is essential to high-speed inspection and spectroscopy applications.

Refractive lensing of scintillating FRBs by subparsec cloudlets in the multiphase CGM

We consider the refractive lensing effects of ionized cool ([Formula: see text]) gas cloudlets in the circumgalactic medium (CGM) of galaxies. In particular, we discuss the combined effects of lensing from these cloudlets and scintillation from plasma screens in the Milky Way interstellar medium (ISM). We show that, if the CGM comprises a mist of subparsec cloudlets with column densities of order [Formula: see text] (as predicted by [M. McCourt, S. P. Oh, R. O'Leary, A. M. Madigan, MNRAS 473, 5407-5431 (2018)]), then fast radio bursts (FRBs) whose sightlines pass within a virial radius of a CGM halo will may be lensed into tens of refractive images with a ∼10 ms scattering timescale. When these images are formed, they will be resolved by scintillating screens in the Milky Way ISM and will suppress the observed scintillation. We illustrate this effect in refractive lensing and argue that positive detections of FRB scintillation may constrain the properties of these cool-gas cloudlets, with current scintillation observation weakly disfavoring the cloudlet model. We propose that sheet-like geometries for the cool gas in the CGM can reconcile quasar absorption measurements (from which we infer the presence of the cool gas with structure on subparsec scales) and the unexpected lack of lensing signals from this gas thus far observed.

Remote sensing of backward reflection from stimulated axion decay

We propose a method for remotely detecting backward reflection via induced decay of cold dark matter such as axion in the background of a propagating coherent photon field. This method can be particularly useful for probing concentrated dark matter streams by Earth’s gravitational lensing effect. Formulae for the stimulated reflection process and the expected sensitivities in local and remote experimental approaches are provided for testing eV scale axion models using broad band lasers. The generic axion-photon coupling is expected to be explorable up to O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(10−12) GeV−1 and O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(10−22) GeV−1 for the idealized local and remote setups, respectively.

Mathematical Modeling of Refraction Characteristics of Electromagnetic Radiation at Stochastic Gravitational Field

Numerical-analytical modeling is used for estimation of gravitational noise influence on propagation of electromagnetic radiation at gravitational field of a group of astrophysical objects. The method bases on numerical integrate of system of light differential equations in the Euler’s form, added differential equations for calculation of statistic moments of side fluctuations of light at a picture plane of observer. The influence of gravitation was taken into account by introducing of the effective refraction index of vacuum, expressed through a gravitational potential. Visions about spatial correlation function of inhomogeneities of effective refraction index of vacuum are used as model. Calculating of gravitation effects of group astrophysical objects are performed under assumption additive contribution of field of every objects in general gravitational field. Modeling of the refraction characteristics of electromagnetic radiation is performed for a various configurations of gravitation field. Results of calculating are shown at a picture plane of observer. The blurring effects of gravitational lensing are investigated at dependence from position of localized area of gravitational noise and astrophysical objects. It’s showed that for case of single-component gravitational field full coverage of object by area of gravitational noise match maximum blurring of lensing effect. The features of gravitational focusing are determined at dependence from position of area noise for asymmetrical twocomponent gravitational field, where one of objects coverage by area of gravitational noise. Offered tool of modeling can be used for both investigation of gravitational lensing of multi-component gravitational field in presence variety of limited area of gravitational noise and under conditions uniform spatial distribution of stochastic gravitational inhomogeneities. Also it can use for recovering of gravitational potentials of non-radiating (hidden) objects by characteristics of received electromagnetic radiation of remote space sources.

Apparently Ultralong Period Radio Signals from Self-lensed Pulsar–Black Hole Binaries

Pulsar–black hole (BH) close binary systems, which have not been found yet, are unique laboratories for testing theories of gravity and understanding the formation channels of gravitational-wave sources. We study the self-gravitational lensing effect in a pulsar–BH system on the pulsar’s emission. Because this effect occurs once per orbital period for almost edge-on binaries, we find that it could generate apparently ultralong period (minutes to hours) radio signals when the intrinsic pulsar signal is too weak to detect. Each of such lensed signals, or “pulse,” is composed of a number of amplified intrinsic pulsar pulses. We estimate that a radio telescope with a sensitivity of 10 mJy could detect a few systems that emit such signals in our Galaxy. The model is applied to three recently found puzzling long-period radio sources: GLEAM-X J1627, PSR J0901-4046, and GPM J1839-10. To explain their observed signal durations and periods, the masses of their lensing components are estimated as ∼104 M ⊙, ∼4 M ⊙, and 103−6 M ⊙, respectively, with their binary coalescence times ranging from a few tens to thousands of years. However, the implied merger rates (as high as ∼103−4 Myr−1 per galaxy) and the large period decay rates (>10−8 s s−1) tend to disfavor this self-lensing scenario for these three sources. Despite this, our work still provides observational characteristics for self-lensed pulsar–BH binaries, which could help the detection of related sources in the future. Finally, for a binary containing a millisecond pulsar and a stellar-mass BH, the Shapiro delay effect would cause a ≥10% variation of the profile width for the subpulses in such lensed signals.

Weak gravitational lensing around dyonic ModMax black hole in plasma

In this study, we examine the effects of weak gravitational lensing and determine the shadow radius around black holes within the Dyonic ModMax (DM) spacetime, also accounting for models with nonuniform plasma distributions. By analyzing various gravitational lens models, we compare corrections to vacuum lensing due to gravitational effects within plasma and plasma inhomogeneity, finding that these effects could be observed in hot gas within galaxy clusters. Starting with the orbits of photons around a black hole in DM, we investigate the shadow and weak gravitational lensing phenomena. Utilizing observational data from the Event Horizon Telescope for M87* and SgrA*, we constrain parameters within DM gravity. To connect our findings to observations, we examine the magnification and positioning of lensed images, along with the weak deflection angle and magnification for sources near different galaxies.

CMBFSCNN: Cosmic Microwave Background Polarization Foreground Subtraction with a Convolutional Neural Network

In our previous study, we introduced a machine learning technique, namely Cosmic Microwave Background Foreground Subtraction with Convolutional Neural Networks (CMBFSCNN), for the removal of foreground contamination in cosmic microwave background (CMB) polarization data. This method was successfully employed on actual observational data from the Planck mission. In this study, we extend our investigation by considering the CMB lensing effect in simulated data and utilizing the CMBFSCNN approach to recover the CMB lensing B-mode power spectrum from multifrequency observational maps. Our method is first applied to simulated data with the performance of the CMB-S4 experiment. We achieve reliable recovery of the noisy CMB Q (or U) maps with a mean absolute difference of 0.016 ± 0.008 μK (or 0.021 ± 0.002 μK) for the CMB-S4 experiment. To address the residual instrumental noise in the foreground-cleaned map, we employ a “half-split maps” approach, where the entire data set is divided into two segments sharing the same sky signal but having uncorrelated noise. Using cross-correlation techniques between two recovered half-split maps, we effectively reduce instrumental noise effects at the power spectrum level. As a result, we achieve precise recovery of the CMB EE and lensing B-mode power spectra. Furthermore, we also extend our pipeline to full-sky simulated data with the performance of the LiteBIRD experiment. As expected, various foregrounds are cleanly removed from the foregrounds contamination observational maps, and recovered EE and lensing B-mode power spectra exhibit excellent agreement with the true results. Finally, we discuss the dependency of our method on the foreground models.

Evolution of Light Absorption Enhancement of Black Carbon Aerosols From Biomass Burning in Atmospheric Photochemical Aging

AbstractThe light absorption enhancement (Eabs) of black carbon (BC) coated with non‐BC materials is crucial in the assessment of radiative forcing, yet its evolution during photochemical aging of plumes from biomass burning, the globe's largest source of BC, remains poorly understood. In this study, plumes from open burning of corn straw were introduced into a smog chamber to explore the evolution of Eabs during photochemical aging. The light absorption of BC was measured with and without coating materials by using a thermodenuder, while the size distributions of aerosols and composition of BC coating materials were also monitored. Eabs was found to increase initially, and then decrease with an overall downward trend. The lensing effect dominated in Eabs at 520 nm, with an estimated contribution percentages of 47.5%–94.5%, which is far greater than light absorption of coated brown carbon (BrC). The effects of thickening and chemical composition changes of the coating materials on Eabs were evaluated through comparing measured Eabs with that calculated by the Mie theory. After OH exposure of 1 × 1010 molecules cm−3 s, the thickening of coating materials led to an Eabs increase by 3.2% ± 1.6%, while the chemical composition changes or photobleaching induced an Eabs decrease by 4.7% ± 0.6%. Simple forcing estimates indicate that coated BC aerosols exhibit warming effects that were reduced after aging. The oxidation of light‐absorbing CxHy compounds, such as polycyclic aromatic hydrocarbons (PAHs), to CxHyO and CxHyO>1 compounds in coating materials may be responsible for the photobleaching of coated BrC.

Enhanced laser performance in an LD end-pumped YAP/Tm:YAP/YAP bonding rod with concave end faces

We demonstrate the effects of thermal bonding and concave end faces on the laser performance of 795 nm LD end-pumped Tm:YAP crystals for the first time. Analysis of the thermal focal length shows that the thermal lensing effect can be effectively compensated by the concave end faces. By combining the thermal bonding with the concave end faces, a maximum output power of 42.5 W is achieved on the concave YAP/Tm:YAP/YAP bonding rod with a negative curvature radius of 500 mm, corresponding to a slope efficiency of 47.4% and an optical-optical (O-O) conversion efficiency of 41.6%. Moreover, the beam quality factors Mx2/My2 are fitted to 1.67/1.69. Compared with the flat YAP/Tm:YAP/YAP bonding rod, the concave YAP/Tm:YAP/YAP bonding rod significantly increases the maximum output power from 36.56 W to 42.5 W, with an approximately 4% improvement in both the slope efficiency and O-O conversion efficiency. These results indicate that the combination of thermal bonding and concave end faces can effectively improve the heat dissipation capacity and mitigate the thermal lensing effect, thereby yielding near-infrared (NIR) laser output with high performance.

Continuous-wave degenerate cavity laser for optical imaging in scattering media.

Lasers play a significant role in optical communication, medical, and scientific research, owing to their high brightness and high coherence. However, the high spatial coherence will lead to specific challenges, such as speckle noise in imaging and wavefront distortion during propagation through scattering media. Here, a continuous-wave (cw) degenerate cavity laser (DCL) with low spatial coherence is demonstrated with efficient suppression of the thermal lensing effect from the gain crystal. Experimentally, a cw degenerate laser output with about 2000 transverse modes corresponding to a speckle contrast of about 0.0224 is achieved. This laser can be used for speckle reduction and is robust against atmospheric turbulence, which may find applications in the field of laser imaging technology and illumination.

Exploring Weak Gravitational Lensing Effects by a Regular Black Hole

Gravitational lensing is one of the physical consequences of Einstein’s general theory of relativity, which has been observationally confirmed. This work aims to study the weak gravitational lensing scenario where the lens is a spherically symmetric, charged-nonsingular black hole that asymptotically behaves as the Reissner-Nordström (RN). The difference exists in the higher-order expansion. Therefore, the metric function of the regular charged black hole is expanded up to the fourth order, and the deflection angle is calculated. The thin lens equation is used, leading to five images: two imaginary and three real images. The exact positions of the images and magnification properties are calculated by providing the physical parameters such as mass, charge, and distances. Our calculation shows that the third image position shifted away from the optical axis. The formalism is applied to the case of a supermassive black hole located at the center of our galaxy with the assumption that it has an electric charge.

Geometric deformation and redshift structure caused by plane gravitational waves

The curved spacetime induced by gravitational waves can give rise to visual effects such as geometric distortions and redshift structures in the observed image. By establishing a mapping from the object's surface coordinates to the observer's screen coordinates, we study these effects in the context of plane gravitational waves. The simulation reveals that the image of an object doesn't merely seem compressed or stretched, but rather appears twisted and wobbled. Furthermore, the redshift structure on the object's surface appears to rotate as a whole. This outcome offers an intuitive depiction of the lensing effect in plane gravitational wave spacetimes.

Testing strong gravitational lensing effects of various supermassive compact objects for the static and spherically symmetric hairy black hole by gravitational decoupling

We investigate the strong gravitational lensing effects of various supermassive compact objects for the static and spherically symmetric hairy black hole by gravitational decoupling. To do this purpose, we first numerically calculate the strong deflection limit coefficients and strong deflection angle with the decoupling modified black hole parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}. It is observed that for the lowest value of the parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}, the strong deflection angle αD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _D$$\\end{document} reaches its maximum value with the parameter β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} and for the lowest value of the parameter β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}, strong deflection angle αD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _D$$\\end{document} reaches its minimum value with the parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}; and also the strong deflection angle for αD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _D$$\\end{document} for the decoupling modified black hole is smaller than standard Schwarzschild black hole (α=0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\alpha =0)$$\\end{document}. We investigate the various astrophysical consequences via strong gravitational lensing by considering the example of various supermassive BHs in the centre nearby galaxies and observe that the decoupling modified black hole could be quantitatively distinguished from the standard Schwarzschild black hole (α=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha =0$$\\end{document}). Findings in our observation suggest that the observational test for a decoupling-modified black hole is indeed feasible.

The gravitational lensing by rotating black holes in loop quantum gravity

In this paper, we explore gravitational lensing effects associated with rotating black holes within the framework of loop quantum gravity. Utilizing the Gauss-Bonnet theorem as extended by Ono et al., we compute the light deflection angle in the weak field limit for a lens that is finitely distanced from both the source and the observer. Our findings indicate that the weak deflection angle for rotating black holes in LQG is smaller than that observed for the classical Kerr black holes, albeit with minimal deviations. In the strong field limit, we determine the photon sphere radius, the light deflection angle, and lensing observables, including the image position θ∞, angular separation s, magnification rmag, and temporal delays among various relativistic images. By considering supermassive black holes, such as Sgr A* and M87*, within the LQG framework, we calculate these observables and investigate the influence of the quantum parameter Aλ on them, compared with the Kerr black hole outcomes. Our comparative analysis reveals that the image position θ∞ and separation s for Sgr A* consistently exceed those for M87*, whereas M87* exhibits considerably greater time delays than Sgr A*. These distinctions could be important in differentiating between rotating black holes in LQG and classical Kerr black holes in future astronomical observations.