On the Physical Nature of Einstein’s Gravitational Lensing Effect

Gravitational lensing has become a powerful research tool for exploring the distribution of matter and energy in the universe nowadays, as glare phenomena around the Sun and massive galaxies are indeed observed on the Earth. What is the physical nature of gravitational lensing effect? Both Newton’s law of gravitation and Einstein’s theory of relativity are difficult to physically explain these glare phenomena. This study points out that the observed glare around the Sun and large galaxies is a result or product of the orthogonal interaction of high-energy particles emitted from different star light sources. It shows a new physical state associated with abnormal high mass-energy density.

Discovery of four gravitational lensing systems by clusters in the SDSS DR6

We report the discovery of 4 strong gravitational lensing systems by visual inspections of the Sloan Digital Sky Survey images of galaxy clusters in Data Release 6 （SDSS DR6）. Two of the four systems show Einstein rings while the others show tangen- tial giant arcs. These arcs or rings have large angular separations （〉 8″） from the bright central galaxies and show bluer color compared with the red cluster galaxies. In addition, we found 5 probable and 4 possible lenses by galaxy clusters.

Cosmic Constraints to the wCDM Model from Strong Gravitational Lensing

We study the cosmic constraint to the wCDM （cold dark matter with a constant equation of state w） model via 118 strong gravitational lensing systems which are compiled from SLA CS, BELLS, LSD and SL2S surveys, where the ratio between two angular diameter distances Dobs =DA（Zl, Zs ） / D A （ O, Zs ） is taken as a cosmic observable. To obtain this ratio, we adopt two strong tensing models： one is the singular isothermal sphere model （SIS） and the other one is the power-law density profile （PLP） model. Via the Markov chain Monte Carlo method, the posterior distribution of the cosmological model parameters space is obtained. The results show that the cosmological model parameters are not sensitive to the parameterized forms of the power-law index γ. Furthermore, the PLP model gives a relatively tighter constraint to the cosmological parameters than that of the SIS model. The predicted value of Ωm = 0.31＋0.44 -0.24 by the SIS model is compatible with that obtained by P1anck2015： Ωm = 0.313 ± 0.013. However, the value of Ωm =0.15＋0.13 -0.11 based on the PLP model is smaller and has 1.25σ tension with that obtained by Planck2015.

Cusp-core problem and strong gravitational lensing

Cosmological numerical simulations of galaxy formation have led to the cuspy density profile of a pure cold dark matter halo toward the center, which is in sharp contradiction with the observations of the rotation curves of cold dark matter-dominated dwarf and low surface brightness disk galaxies, with the latter tending to favor mass profiles with a flat central core. Many efforts have been devoted to resolving this cusp-core problem in recent years, among them, baryon-cold dark matter interactions are considered to be the main physical mechanisms erasing the cold dark matter （CDM） cusp into a flat core in the centers of all CDM halos. Clearly, baryon-cold dark matter interactions are not customized only for CDM-dominated disk galaxies, but for all types, including giant ellipticals. We first fit the most recent high resolution observations of rotation curves with the Burkert profile, then use the constrained core size-halo mass relation to calculate the lensing frequency, and compare the predicted results with strong lensing observations. Unfortunately, it turns out that the core size constrained from rotation curves of disk galaxies cannot be extrapolated to giant ellipticals. We conclude that, in the standard cosmological paradigm, baryon-cold dark matter interactions are not universal mechanisms for galaxy formation, and therefore, they cannot be true solutions to the cusp-core problem.

Constraining Equation of State of Dark Matter:Including Weak Gravitational Lensing

Usually the equation of state （EoS） of dark matter is zero when it is cold, however there exists the possibility of a （effective） nonzero EoS of dark matter due to its decay and interaction with dark energy. In this work, we try to constrain the EoS of dark matter/JAdm using the currently available cosmic observations which include the geometrical and dynamical measurements. For the geometrical measurements, the luminosity distance of type Ia supernovae, the angular diameter distance and comoving sound horizon from baryon acoustic oscillations and the cosmic microwave background radiation will be employed. The data points from the redshift-space distortion and weak gravitational lensing will be taken as dynamical measurements. Using the Markov chain Monte Carlomethod, we obtain a very tight constraint on the-EoS of dark matter：wdm=0.0000532 ＋0.000692＋0.00136＋0.00183 -0.000686-0.00136-0.00177.

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 A. We apply a numerical method to evaluate the deflection angle of bending light rays, image locations θ of sample sourceβ = π- 4, and corresponding magnifications μ. There are no obtained real values for Einstein ring locations θE（β = 0） 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 ∈ = 16AM2 /2The 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 0.001 〈 ∈ 〈 0.01.

Regular Magnetic Black Hole Gravitational Lensing

The Bronnikov regular magnetic black hole as a gravitational lens is studied. In nonlinear electrodynamics, photons do not follow null geodesics of background geometry, but move along null geodesics of a corresponding effective geometry. To study the Bronnikov regular magnetic black hole gravitational lensing in the strong deflection limit, the corresponding effective geometry should be obtained firstly. This is the most important and key step. We obtain the deflection angle in the strong deflection limit, and further calculate the angular positions and magnifications of relativistic images as well as the time delay between different relativistic images. The influence of the magnetic charge on the black hole gravitational tensing is also discussed.

Effects of Homogeneous Plasma on Strong Gravitational Lensing of Kerr Black Holes

Considering the Kerr black hole surrounded by a homogeneous unmagnetized plasma medium, we study the strong gravitational lensing on the equatorial plane of the Kerr black hole. It is found that the presence of the uniform plasma can increase the photon-sphere radius r_{／rm ps}, the coefficients ／bar{a} and ／bar{b}, the angular position of the relativistic images （／theta_{／infty}）, the deflection angle ／alpha（／theta） and the angular separation s. However, the relative magnitude r_{／rm m} decreases in the presence of the uniform plasma medium. It is also shown that the impact of the uniform plasma on the effect of strong gravitational lensing becomes smaller as the spin of the Kerr black hole increases in the prograde orbit （a〉0）. In particular, for the extreme black hole （a=0.5）, the effect of strong gravitational lensing in the homogeneous plasma medium is the same as the case in vacuum for the prograde orbit.

Mass to light ratio of galaxies and gravitational lensing

We investigate the potential of constraining the mass to light ratio of field galaxies using weak lensing shear and flexions. A suite of Monte Carlo simulations are used to generate weak lensing observations with different noise models. Using mock data, we find that the inclusion of flexions can improve the estimate of foreground halo parameters, but the details are strongly dependent on noise in the model. In the intrinsic noise limit, both shear and flexions are promising tools to study the mass to light ratio of galaxies. However, if the noise model of flexions follows the form described by Rowe et al., there is only - 5% improvement in the constraints even with next generation lensing observations.

Gravitational lensing properties of an isothermal universal halo profile

N-body simulations predict that dark matter halos with different mass scales are described by a universal model, the Navarro-Frenk-White （NFW） den- sity profiles. As a consequence of baryonic cooling effects, these halos will become more concentrated, and similar to an isothermal sphere over a large range in radii （～ 300 h-1 kpc）. The singular isothermal sphere （SIS） model however has to be trun- cated artificially at large radii since it extends to infinity. We model a massive galaxy halo as a combination of an isothermal sphere and an NFW density profile. We give an approximation for the mass concentration at different baryon fractions and present exact expressions for the weak lensing shear and flexion for such a halo. We compare the lensing properties with the SIS and NFW profiles. We find that the combined pro- file can generate higher order lensing signals at small radii and is more efficient in generating strong lensing events. In order to distinguish such a halo profile from the SIS or NFW profiles, one needs to combine strong and weak lensing constraints for small and large radii.

Probing the dark side of the Universe with weak gravitational lensing effects

Arising from gravitational deflections of light rays by large-scale struc- tures in the Universe, weak-lensing effects have been recognized as one of the most important probes in cosmological studies. In this paper, we review the main progress in weak-lensing analyses, and discuss the challenges in future investigations aiming to understand the dark side of the Universe with unprecedented precisions.

The Amplitude of Mass Fluctuations and Mass Density of the Universe Constrained by Strong Gravitational Lensing

We investigate the linear amplitude of mass fluctuations in the universe, σ8, and the present mass density parameter of the Universe, Ωm, from statistical strong gravitational lensing. We use the two population model of lens halos with fixed cooling mass scale Mc = 3×1013h-1M⊙ to match the observed lensing probabilities, and leave σ8 orΩm as a free parameter to be constrained by the data. Another varying parameter, the equation of state of dark energy ω, and its typical values of -1, -2/3, -1/2 and -1/3 are investigated. We find that σ8 is degenerate with Ωm in a way similar to that suggested by present day cluster abundance as well as cosmic shear lensing measurements: σ8Ω0.6m≈0.33. However, both σ8≤0.7 and Ωm≤0.2 can be safely ruled out, the best fit is when σ8 = 1.0, Ωm = 0.3 and ω= - 1. This result is different from that obtained by Bahcall & Bode, who gave σ8 = 0.98±0.1 and Ωm = 0.17 ±0.05. For σ8 = 1.0, the higher value ofΩm = 0.35 requires ω = -2/3 and Ωm = 0.40 requires ω= -1/2.

Is the Variable X-ray Source in M82 due to Gravitational Lensing?

We explore the possibility of attributing the recent discovery of the variable hard X-ray source CXO M82 J095550.2+694047 in M82 to the gravitational magnification by an intervening stellar object along the line of sight acting as a microlens. The duration of the event (> 84 days) allows us to set robust constraints on the mass and location of the microlensing object when combined with the dynamical properties of the Galactic halo, M82 and typical globular clusters. Except for the extremely low probability, the microlensing magnification by MACHO in either the Galactic halo or M82 halo is able to explain the X-ray variability of CXO M82 J095550.2+694047. It is hoped that the lensing hypothesis can be tested soon by measurement of the light curve.

A Remark on Using Gravitational Lensing Probability as a Probe of the Central Regions of CDM Halos

We calculate the gravitational lensing probabilities by cold dark matter (CDM) halos with different density profiles, and compare them with current observations from the Cosmic Lens All-Sky Survey (CLASS) and the Jodrell-Bank VLA Astrometric Survey (JVAS). We find that the lensing probability is dramatically sensitive to the clumping of the dark matter, or quantitatively, the concentration parameter. We also find that our predicted lensing probabilities in most cases show inconsistency with the observations. It is argued that high lensing probability may not be an effective tool for probing the statistical properties of inner structures of dark matter halos.

Gravitational Lensing by Spherical Lenses

In this work we introduced a new proposal to study the gravitational lensing theory by spherical lenses, starting from its surface mass density ∑(x) written in terms of a decreasing function f of a dimensionless coordinate x on the lens plane. The main result is the use of the function f(x) to find directly the lens properties, at the same time that the lens problem is described by a first order differential equation which encodes all information about the lens. SIS and NIS profiles are used as examples to find their functions f(x). Using the Poisson equation we find that the deflection angle is directly proportional to f(x), and therefore the lens equation can be written in terms of the function and the parameters of the lens. The critical and caustic curves, as well as image formation and magnification generated by the lens are analyzed. As an example of this method, the properties of a lens modeled by a NFW profile are determined. Although the puntual mass is spherically symmetric, its mass density is not continuous so that its f(x) function is discussed in Appendix 1.

Strong gravitational lensing of blazar gamma-radiation and intergalactic magnetic fields

The influence of intergalactic magnetic fields on the strong gravitational lensing of blazar secondary gamma radiation is discussed.Currently,two cases of strong gravitational lensing of blazar gamma-radiation are known,where radiation is deflected by galaxies on the line of sight between the blazars and Earth.The magnetic field can affect the movements of electron-positron pairs generated by primary radiation,thereby changing the directions of secondary gamma radiation.It modifies the equation of the gravitational lens and leads to the dependence of the observed signal in the secondary gamma radiation on the energy of photons and magnetic field.Accordingly,it is possible,in principle,to estimate the intergalactic magnetic fields from the time delay of signals,from the angular position of images(for future high-resolution gamma-ray telescopes)or from the shape of the observed energy spectrum.This method is demonstrated by the example of the blazar B0218+357.In this case,however,it is not possible to obtain useful constraints due to the large distances to the blazar and lens galaxy.The result is only a lower limit on the magnetic field B>2×10^(−17)G,which is weaker than other existing constraints.However,future discoveries of lensed blazars may provide more favorable opportunities for measuring the magnetic fields,especially with the help of a new generation of gamma-ray telescopes such as e-ASTROGAM,GECAM,and SVOM as well as future gamma-ray telescopes with a high angular resolution,∼0.1″.

Determination of the spin parameter and the inclination angle from the primary and secondary images caused by gravitational lensing

We study the primary images(PIs)and secondary images(SIs)caused by strong gravitational lensing around a Kerr black hole shadow,which carry some essential signatures related to the black hole space-time.We define a new celestial coordinate,whose origin is the center of the black hole shadow,to locate the PIs and SIs of luminous celestial objects.Based on the dragging effect caused by the rotating black hole and the inclination angle of the observer,the relative positions between the PIs and SIs are different for different values of the Kerr spin parameter a and the observer's inclination angle i;hence,it can be used to determine the values of a and i.We propose a specific approach to measure a and i using the PIs and SIs.The time delays between the PIs and SIs are different for different values of a and i.The time delays,in conjunction with the relative positions between the PIs and SIs,can enable us to measure a and i more precisely.These PIs and SIs around the black hole shadow act as unique fingerprints for the black hole space-time,using which we can further determine other parameters of different types of compact objects and verify various theories of gravity.Our results provide a new method to implement parameter estimation in the study of black hole physics and astrophysics.

Strong gravitational lensing of rotating regular black holes in non-minimally coupled Einstein-Yang-Mills theory

The strong gravitational lensing of a regular and rotating magnetic black hole in non-minimally coupled Einstein-Yang-Mills theory is studied.We find that,with the increase of any characteristic parameters of this black hole,such as the rotating parameter a,magnetic charge q and EYM parameterλ,the angular image positionθ∞and relative magnification rm decrease while deflection angleα(θ)and image separation s increase.The results will degenerate to that of the Kerr case,RN case with magnetic charge and Schwarzschild case when we take some specific values for the black hole parameters.The results also show that,due to the small influence of magnetic charge and EYM parameters,it is difficult for current astronomical instruments to tell this black hole apart from a General Relativity one.

Photon motion and weak gravitational lensing in black-bounce spacetime

The effect of spacetime curvature on photon motion may offer an opportunity to propose new tests on gravity theories.In this study,we investigate and focus on the massless(photon)particle motion around blackbounce gravity.We analyze the horizon structure around a gravitational compact object described by black-bounce spacetime.The photon motion and the effect of gravitational weak lensing in vacuum and plasma are discussed,and the shadow radius of the compact object is also studied in black-bounce spacetime.Additionally,the magnification of the image is studied using the deflection angle of light rays.

Strong gravitational lensing for photon coupled to Weyl tensor in Kiselev black hole

The objective of the present work is to highlight the phenomena of strong gravitational lensing and deflection angle for the photon coupling with the Weyl tensor in a Kiselev black hole.Here,we have extended the prior work of Chen and Jing(S.Chen and J.Jing,JCAP,10:002(2015))for a Schwarzschild black hole to a Kiselev black hole.For this purpose,the equation of motion for the photons coupled to the Weyl tensor,null geodesic,and equation of photon sphere in a Kiselev black hole spacetime have been formulated.It is found that the equation of motion of the photons depends not only on the coupling between the photons and the Weyl tensor,but also on the polarization direction of the photons.There is a critical value of the coupling parameter,α,for the existence of the marginally circular photon orbit outside the event horizon,which depends on the parameters of the black hole and the polarization direction of the photons.Further,the polarization directions of the coupled photons and the coupling parameter,α;both modify the features of the photon sphere,angle of deflection,and functions(^ˉa and^ˉb)owing to the strong gravitational lensing in the Kiselev black hole spacetime.In addition to this,the observable gravitational lensing quantities and the shadows of the Kiselev black hole spacetime are presented in detail.