Weak Deflection Research Articles

Light deflection angle by generalized Dymnikova black hole

The gravitational lensing caused by a generalized Dymnikova black hole in weak field conditions is examined in this work. The optical geometry of such a black hole is first examined, and then the Gauss–Bonnet theorem is used to calculate the deflection angle in weak field limitations. Moreover, the effect of black hole mass, the parameters [Formula: see text] and [Formula: see text] on the deflection angle in leading order terms are probed. Otherwise, we explore the implication of the plasma medium on the weak deflection angle behavior.

Weak deflection angle and shadow cast by the charged-Kiselev black hole with cloud of strings in plasma* *Partly supported by the Uzbekistan Ministry for Innovative Development (FZ-20200929344 and F-FA-2021-510). I.H. is grateful to the Institute of Mathematics, University of Aberdeen, Scotland, UK, where a part of this study was done under the IMU-CDC Individual Travel Support Program. G.M. is supported

In this study, the gravitational deflection angle of photons in the weak field limit (or the weak deflection angle) and shadow cast by the electrically charged and spherically symmetric static Kiselev black hole (BH) in the string cloud background are investigated. The influences of the BH charge Q, quintessence parameter γ, and string cloud parameter a on the weak deflection angle are studied using the Gauss-Bonnet theorem, in addition to studying the influences on the radius of photon spheres and size of the BH shadow in the spacetime geometry of the charged-Kiselev BH in string clouds. Moreover, we study the effects of plasma (uniform and non-uniform) on the weak deflection angle and shadow cast by the charged-Kiselev BH surrounded by the clouds of strings. In the presence of a uniform/nonuniform plasma medium, an increase in the string cloud parameter a increases the deflection angle α. In contrast, a decrease in the BH charge Q decreases the deflection angle. Further, we observe that an increase in the BH charge Q causes a decrease in the size of the shadow of the BH. We notice that, with an increase in the values of the parameters γ and a, the size of the BH shadow increases, and therefore, the intensity of the gravitational field around the charged-Kiselev BH in string clouds increases. Thus, the gravitational field of the charged-Kiselev BH in the string cloud background is stronger than the field produced by the pure Reissner-Nordstrom BH. Moreover, we use the data released by the Event Horizon Telescope (EHT) collaboration, for the supermassive BHs M87* and Sgr A*, to obtain constraints on the values of the parameters γ and a.

Generalized Extended Uncertainty Principle Black Holes: Shadow and Lensing in the Macro- and Microscopic Realms

Motivated by the recent study about the extended uncertainty principle (EUP) black holes, we present in this study its extension called the generalized extended uncertainty principle (GEUP) black holes. In particular, we investigated the GEUP effects on astrophysical and quantum black holes. First, we derive the expression for the shadow radius to investigate its behavior as perceived by a static observer located near and far from the black hole. Constraints to the large fundamental length scale, L*, up to two standard deviations level were also found using the Event Horizont Telescope (EHT) data: for black hole Sgr. A*, L*=5.716×1010 m, while for M87* black hole, L*=3.264×1013 m. Under the GEUP effect, the value of the shadow radius behaves the same way as in the Schwarzschild case due to a static observer, and the effect only emerges if the mass, M, of the black hole is around the order of magnitude of L* (or the Planck length, lPl). In addition, the GEUP effect increases the shadow radius for astrophysical black holes, but the reverse happens for quantum black holes. We also explored GEUP effects to the weak and strong deflection angles as an alternative analysis. For both realms, a time-like particle gives a higher value for the weak deflection angle. Similar to the shadow, the deviation is seen when the values of L* and M are close. The strong deflection angle gives more sensitivity to GEUP deviation at smaller masses in the astrophysical scenario. However, the weak deflection angle is a better probe in the micro world.

Deflection Angle and Shadow of the Reissner–Nordström Black Hole with Higher-Order Magnetic Correction in Einstein-Nonlinear-Maxwell Fields

Nonlinear electrodynamics is known as the generalizations of Maxwell electrodynamics at strong fields and presents interesting features such as curing the classical divergences present in the linear theory when coupled to general relativity. In this paper, we consider the asymptotically flat Reissner–Nordström black hole solution with higher-order magnetic correction in Einstein-nonlinear-Maxwell fields. We study the effect of the magnetic charge parameters on the black hole, viz., weak deflection angle of photons and massive particles using the Gauss–Bonnet theorem. Moreover, we apply Keeton–Petters formalism to confirm our results concerning the weak deflection angle. Apart from a vacuum, their influence in the presence of different media such as plasma and dark matter are probed as well. Finally, we examine the black hole shadow cast using the null-geodesics method and investigate its spherically in-falling thin accretion disk. Our inferences show how the magnetic charge parameter p affects the other physical quantities; so, we impose some constraints on this parameter using observations from the Event Horizon Telescope.

Gravitational Faraday Rotation of gravitational waves by a Kerr black hole

Gravitational Faraday Rotation (GFR) is a frame-dragging effect induced by rotating massive objects, which is one of the important, yet studied characteristics of lensed gravitational waves (GWs). In this work, we calculate the GFR angle χ g of GWs in the weak deflection limit, assuming it is lensed by a Kerr black hole (BH). We find that the GFR effect changes the initial polarization state of the lensed GW. Compared with the Einstein deflection angle, the dominant term of the rotation angle χ g is a second-order correction to the polarization angle, which depends on the light-of-sight component of BH angular momentum. Such a rotation is tiny and degenerates with the initial polarization angle. In some critical cases, the GFR angle is close to the detection capability of the third-generation GW detector network, although the degeneracy has to be broken.

Probing effective loop quantum gravity on weak gravitational lensing, Hawking radiation and bounding greybody factor by black holes

In this paper, we study the weak deflection angle of black hole in effective loop quantum gravity using the geometrical technique used by Gibbons and Werner. We first derive the optical metric, calculate the Gaussian optical curvature, and then apply the Gauss-Bonnet theorem. We then also investigate the effect of plasma and dark matter mediums on the weak deflection angle. We show that increasing the impact of these two mediums grows the deflection angle. We also calculate the Hawking temperature via Gauss-Bonnet theorem. In addition, we determine the fermionic greybody bounds. Moreover, we discuss the graphical behaviour of the deflection angle and bounds on the greybody factor. Graphically, we observe that taking $0 < A_{\lambda} < 1$ angle ranges from negative values to maximum values and also attain maximum value for these values of $ A_{\lambda}$ and for $A_{\lambda} \geq 1$ exponentially approaches to zero. Later, we graphically investigate that the greybody factor bound exhibits the convergent behaviour by converging to $1$. We also examine that the results obtained for the black hole in effective loop quantum gravity are reduced to the Schwarzschild black hole solutions when the dimensionless non-negative parameter is equal to zero $A_{\lambda}=0$.

Dehnen halo effect on a black hole in an ultra-faint dwarf galaxy

There had been recent advancement toward the detection of ultra-faint dwarf galaxies, which may serve as a useful laboratory for dark matter exploration since some of them contains almost 99% of pure dark matter. The majority of these galaxies contain no black hole that inhabits them. Recently, there had been reports that some dwarf galaxies may have a black hole within. In this study, we construct a black hole solution combined with the Dehnen dark matter halo profile, which is commonly used for dwarf galaxies. We aim to find out whether there would be deviations relative to the standard black hole properties, which might allow determining whether the dark matter profile in an ultra-faint dwarf galaxy is cored or cuspy. To make the model more realistic, we applied the modified Newman-Janis prescription to obtain the rotating metric. We analyzed the black hole properties such as the event horizon, ergoregion, geodesics of time-like and null particles, and the black hole shadow. Using these observables, the results indicate the difficulty of distinguishing whether the dark matter is cored or cuspy. To find an observable that can potentially distinguish these two profiles, we also calculated the weak deflection angle to examine the effect of the Dehnen profile in finite distance and far approximation. Our results indicate that using the weak deflection angle is far better, in many orders of magnitude, in potentially differentiating these profiles. We conclude that although dwarf galaxies are dark matter-dominated places, the effect on the Dehnen profile is still dependent on the mass of the black hole, considering the method used herein.

Gravitational lensing for power-Maxwell charged quintessence black hole in Rastall gravity

In this paper, we investigate the gravitational lensing for power-Maxwell charged quintessence black hole (BH) without cosmological constant in Rastall’s theory of gravity in both the strong-field limit and weak-field limit. Furthermore, we discuss the gravitational lensing by the linear electrodynamic (LE) and nonlinear electrodynamic (NLE) Maxwell field with the equation of state (EoS) parameter of the quintessence ([Formula: see text]) and compared to the case with Einstein’s gravity. We discuss the behaviors of the photon sphere radius [Formula: see text], impact parameter [Formula: see text], strong lensing coefficients [Formula: see text], [Formula: see text] and the deflection angle [Formula: see text] on the equatorial plane [Formula: see text] with the different values of Rastall parameter [Formula: see text] for the case of LE and NLE Maxwell field in the strong field limit. We also investigate the angular separation [Formula: see text], angular position [Formula: see text] and the magnification of the relativistic images. Further, we also study about the weak lensing BHs in Rastall gravity. We investigate the behaviors of weak deflection angle with the different values of Rastall parameter [Formula: see text] for the case of LE and NLE Maxwell field in the weak-field limit.

Effect of Horndeski theory on weak deflection angle using the Gauss–Bonnet theorem

The main goal of this paper is to study the weak gravitational lensing by Horndeski black hole in weak field approximation. In order to do so, we exploit the Gibbons–Werner method to the optical geometry of Horndeski black hole and implement the Gauss–Bonnet theorem to accomplish the deflection angle of light in weak field region. Furthermore, we have endeavored to extend the scale of our work by comprising the impact of plasma medium on the deflection angle as properly. Later, the graphical influence of the deflection angle of photon on Horndeski black hole in plasma and nonplasma medium is examined.

Shadow and Weak Deflection Angle of a Black Hole in Nonlocal Gravity

Black hole shadow and gravitational lensing play important roles in testing gravitational theories in the strong field regime. As the first-order modifications from quantum gravity, the nonlocality can be manifested by black hole shadow and gravitational lensing. For example, the nonlocal parameter introduced by nonlocality will affect the shape and size of the black hole shadow, and also affect the deflection angle of light rays. In this paper, we mainly investigate the effects of the nonlocality on the black hole shadow and the gravitational lensing for two types of rotating black holes in nonlocal gravity. It is found that the size of the black hole shadow decreases with the nonlocal parameter since the nonlocality weakens the gravitational constant, and the shape of the shadow becomes more deformed with the increase in the nonlocal parameter. However, if the rotation parameter is small, the shape of the shadow is almost a circle even though the nonlocal parameter approaches its maximum. The energy emission rate in both models is also studied. The results show that there is a peak for each curve and the peak decreases and shifts to the low frequency with the increase in the nonlocal parameter. In addition, we also explore the shadow of both types of black holes surrounded by a nonmagnetized pressureless plasma which satisfies the separability condition. It is found that the plasma has a frequency-dependent dispersive effect on the size and shape of the black hole shadow. For the gravitational lensing, we find that the nonlocal parameter of model A makes a positive contribution to the deflection angle, which can be compared with the contribution of the rotation parameter, while the nonlocal parameter of model B makes a negative contribution which can be ignored. These results may be helpful for probing nonlocal gravity in future observations.

Gravitational lensing by a black-bounce-Reissner–Nordström spacetime

We investigate the weak and strong deflection gravitational lensing by a black-bounce-Reissner–Nordström spacetime and obtain their lensing observables. Assuming the supermassive black holes in the Galactic Center and at the center of M87, Sgr A* and M87* respectively, as the lenses, we evaluate these observables and assess their detectability. We also intensively compare these lensing signatures with those of various tidal or charged spacetimes. We find that it might be possible to distinguish these spacetimes by measuring the fluxes difference of the lensed images by Sgr A* in its quiet stage.

Dark matter effect on the weak deflection angle by black holes at the center of Milky Way and M87 galaxies

In this paper, we investigated the effect of dark matter on the weak deflection angle by black holes at the galactic center. We consider three known dark matter density profiles such as the Cold Dark Matter, Scalar Field Dark Matter, and the Universal Rotation Curve from the Burkert profile. To achieve this goal, we used how the positional angles are measured by the Ishihara et al. method based on the Gauss–Bonnet theorem on the optical metric. With the help of the non-asymptotic form of the Gauss-Bonnet theorem, the longitudinal angle difference is also calculated. First, we find the emergence of apparent divergent terms on the said profiles, which indicates that the spacetime describing the black hole-dark matter combination is non-asymptotic. We showed that these apparent divergent terms vanish when the distance of the source and receiver are astronomically distant from the black hole. Using the current observational data in the Milky Way and M87 galaxies, we find interesting behaviors of how the weak deflection angle varies with the impact parameter, which gives us some hint on how dark matter interacts with the null particles for each dark matter density profile. We conclude that since these deviations are evident near the dark matter core radius, the weak deflection angle offers a better alternative for dark matter detection than using the deviation from the black hole shadow. With the dark matter profiles explored in this study, we find that the variation of the values for weak deflection angle strongly depends on the dark matter mass on a particular profile.

Weak Deflection Angle and Greybody Bound of Magnetized Regular Black Hole

In this paper, we examine the weak deflection angle and greybody bound for a magnetized regular black hole. For this purpose, we apply the Gauss–Bonnet theorem on the black hole and obtain the deflection angle in plasma and non-plasma mediums. Moreover, we investigate graphically the effect of impact parameter on the deflection angle for regular black hole in both mediums. We examine that the deflection angle goes to infinity when the impact parameter approaches zero. We also observe that the deflection angle shows negative behaviour at q=0.6 and q=2.09, but at 0.6&lt;q&lt;2.09, the angle shows positive behaviour. Furthermore, we study the rigorous bound phenomenon of the greybody factor in the background for a magnetized regular black hole. Later, we analyse the graphical behaviour of greybody bound with respect to different values of ω and observe that, at small values of ω, the bound increases, but for large values, the bound decreases. After that, we examine that, when we put G=1, l=0 and q=0, all results for the magnetized regular black hole solution reduce into results of the Schwarzschild black hole solution.

Bounding greybody and deflection angle of improved Schwarzschild black hole

In this paper, we study the weak deflection angle in the spacetime of improved Schwarzschild black hole using the method derived by Gibbons and Werner. To do so, we derive the optical curvature from the optical metric and calculate deflection angle in weak field limits by using the Gauss–Bonnet theorem. Moreover, we study the effect of the plasma medium on the weak gravitational lensing using the Gauss–Bonnet theorem. Furthermore, we also study the graphical analysis of the deflection angle in both the plasma and non-plasma mediums. Moreover, we obtain the bound on greybody for improved Schwarzschild black hole.

Effect of the magnetic charge on weak deflection angle and greybody bound of the black hole in Einstein-Gauss-Bonnet gravity

The objective of this paper is to analyze the weak deflection angle of Einstein-Gauss-Bonnet gravity in the presence of plasma medium. To attain our results, we implement the Gibbons and Werner approach and use the Gauss-Bonnet theorem to Einstein gravity to acquire the resulting deflection angle of photon's ray in the weak field limit. Moreover, we illustrate the behavior of plasma medium and non-plasma mediums on the deflection of photon's ray in the framework of Einstein-Gauss-Bonnet gravity. Similarly, we observe the graphical influences of deflection angle on Einstein-Gauss-Bonnet gravity with the consideration of both plasma and non-plasma mediums. Later, we observe the rigorous bounds phenomenon of the greybody factor in contact with Einstein-Gauss-Bonnet gravity and calculate the outcomes, analyze graphically for specific values of parameters.

Weak deflection angle of light in two classes of black holes in nonlinear electrodynamics via Gauss–Bonnet theorem

In this paper, we study the gravitational lensing by some black hole classes within the nonlinear electrodynamics in weak field limits. First, we calculate an optical geometry of the nonlinear electrodynamics black hole and then we use the Gauss–Bonnet theorem for finding deflection angle in weak field limits. The effect of nonlinear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

Weak deflection angle of Kazakov–Solodukhin black hole in plasma medium using Gauss–Bonnet theorem and its greybody bonding

In this paper, we study light rays in a Kazakov-Solodukhin black hole. To this end, we use the optical geometry of the Kazakov-Solodukhin black hole within the Gauss-bonnet theorem. We first show the effect of the deformation parameter $a$ on the Gaussian optical curvature, and then we use the modern method popularized by Gibbons and Werner to calculate the weak deflection angle of light. Our calculations of deflection angle show how gravitational lensing is affected by the deformation parameter $a$. Moreover, we demonstrate the effect of a plasma medium on weak gravitational lensing by the Kazakov-Solodukhin black hole. We discuss that the increasing the deformation parameter $a$, will increase the weak deflection angle of the black hole. Our analysis also uncloak how one may find a observational evidence for a deformation parameter on the deflection angle. In addition, we studied the rigorous bounds of the Kazakov-Solodukhin black hole for the grey body factor and also studied the graphical behaviour of the bounds by fixing $l=0$ and $M=1$ and observed that increasing the deformation parameter $a$ will decrease the rigorous bound $T_b$ of the black hole.

Schwarzschild-like black hole with a topological defect in bumblebee gravity

In this paper, we derive an exact black hole spacetime metric in the Einstein–Hilbert–Bumblebee (EHB) gravity around global monopole field. We study the horizon, temperature, and the photon sphere of the black hole. Using the null geodesics equation, we obtain the shadow cast by the Schwarzschild-like black hole with a topological defect in bumblebee gravity. Interestingly, the radius of shadow of the black hole increases with increase in the global monopole parameter. We also visualize the shadows and energy emission rates for different values of parameters. Moreover, using the Gauss–Bonnet theorem, we calculate the deflection angle in weak field limits and we discuss the possibility of testing the effect of global monopole field and bumblebee field, on a weak deflection angle. We find that the global monopole parameter and also Lorentz symmetry breaking parameter has an increasing effect on the deflection angle.

Shadow and weak deflection angle of extended uncertainty principle black hole surrounded with dark matter

In this paper, we discuss the possible effects of dark matter on a Schwarzschild black hole with the correction of extended uncertainty principle (EUP), such as the parameter α and the large fundamental length scale L∗. In particular, we surround the EUP black hole of mass m with a static spherical shell of dark matter described by the parameters mass M, inner radius rs, and thickness Δrs. In this study, we find that there is no deviation in the event horizon, which readily implies that the black hole temperature due to the Hawking radiation is independent of any dark matter concentration. In addition, we show some effects of the EUP parameter on the innermost stable circular orbit (ISCO) radius of time-like particles, photon sphere, shadow radius, and weak deflection angle. It is found that time-like orbits are affected by deviation of low values of mass M. A greater dark matter density is needed to have remarkable effects on the null orbits. Using the analytic expression for the shadow radius and the approximation Δrs>>rs, it is revealed that L∗ should not be lower than 2m. To broaden the scope of this study, we also calculate the analytic expression for the weak deflection angle using the Ishihara et al. method (Ishihara et al., 2016). As a result, we show that Δrs is improved by a factor of (1+4αm2/L∗2) due to the EUP correction parameters. The calculated shadow radius and weak deflection angle are then compared using the estimated values of the galactic mass from Sgr A*, M87, and UGC 7232, as well as the mass of the supermassive black hole at their center.

Weak Deflection Angle and Shadow by Tidal Charged Black Hole

In this article, we calculate the deflection angle of a tidal charged black hole (TCBH) in weak field limits. First, we obtain the Gaussian optical curvature and then apply the Gauss–Bonnet theorem on it. With the help of Gibbons–Werner method, we are able to calculate the light’s deflection angle by TCBH in weak field limits. After calculating the deflection angle of light, we check the graphical behavior of TCBH. Moreover, we further find the light’s deflection angle in the presence of the plasma medium and also check the graphical behavior in the presence of the plasma medium. Moreover, we investigate the shadow of TCBH. For calculating the shadow, we first find the null geodesics around the TCBH and then find its shadow radius. We also obtain TCBH’s shadow in the plasma medium. Hence, we discuss the shadow of the TCBH, using the M87* parameters announced by the event horizon telescope.