Strong Field Gravitational Lensing Research Articles

Gravitational lensing and shadow of charged black holes in the low-energy limit of string theory

In this work, we investigate the shadow cast and strong field gravitational lensing of a new class of black hole solutions in dilaton gravity where dilaton field is coupled with nonlinear Maxwell invariant [Younesizadeh et al. in Int J Mod Phys A 34(35):1950239]. The space-time is a stationary axisymmetric geometry. The key part in our investigations is finding the effect of dilaton parameter N on the size of shadows and the energy emission rate. As the N parameter increases, the size of black hole shadow increases. Also, the energy emission rate increases with increase in the dilaton parameter N. By supposing the gravitational field of the supermassive object at the heart of Milky Way galaxy described by this metric, we estimated the numerical values of the observables for gravitational lensing in the strong field limit.

Strong gravitational lensing by rotating Simpson-Visser black holes

We investigate strong field gravitational lensing by rotating Simpson-Visser black hole, which has an additional parameter (0 ≤ l/2M ≤ 1), apart from mass (M) and rotation parameter (a). A rotating Simpson-Visser metric correspond to (i) a Schwarzschild metric for l/2M = a/2M = 0 and M ≠ 0, (ii) a Kerr metric for l/2M = 0, |a/2M| < 0.5 and M ≠ 0 (iii) a rotating regular black hole metric for |a/2M| < 0.5, M ≠ 0 and l/2M in the range 0 < l/2M < 0.5 + √((0.5)2-(a/2M)2), and (iv) a traversable wormhole for a |a/2M | > 0.5 and l/2M ≠ 0. We find a decrease in the deflection angle α D and also in the ratio of the flux of the first image and all other images r mag. On the other hand, angular position θ1 increases more slowly and photon sphere radius x m decreases more quickly, but angular separation s increases more rapidly, and their behaviour is similar to that of the Kerr black hole. The formalism is applied to discuss the astrophysical consequences in the supermassive black holes NGC 4649, NGC 1332, Sgr A* and M87* and find that the rotating Simpson-Visser black holes can be quantitatively distinguished from the Kerr black hole via gravitational lensing effects. We find that the deviation of the lensing observables Δθ1 and Δs of rotating Simpson Visser black holes from Kerr black hole for 0 < l/2M < 0.6 (a/2M = 0.45), for supermassive black holes Sgr A* and M87, respectively, are in the range 0.0422–0.11658 μas and 0.031709–0.08758 μas while |Δr mag| is in the range 0.2037 – 0.95668. It is difficult to distinguish the two black holes because the departure are in \U0001d4aa(μas), which are unlikely to get resolved by the current EHT observations, and one has to wait for future observations by ngEHT can pin down the exact constraint.We also derive a two-dimensional lens equation and formula for deflection angle in the strong field limit by focusing on trajectories close to the equatorial plane.

Strong field gravitational lensing by hairy Kerr black holes

Recent times witnessed a surge of interest in strong gravitational lensing by black holes due to the Event Horizon Telescope (EHT) results, which suggest comparing the black hole lensing in general relativity and modified gravity theories. This may help us to assess the phenomenological differences between these models. A Kerr black hole is also a solution to some alternative theories of gravity, while recently obtained modified Kerr black holes (hairy Kerr black holes), which evade the no-hair theorem, are due to additional sources from surrounding fluid, like dark matter, having conserved energy momentum tensor (EMT). These hairy Kerr black holes may also be solutions to an alternative theory of gravity. We generalize previous work on gravitational lensing by a Kerr black hole in the strong deflection limits to the hairy Kerr black holes, with a deviation parameter $\alpha$ and a primary hair $\ell_0$. Interestingly, the deflection coefficient $\bar{a}$ increases and decreases with increasing $\ell_0$ and $\alpha$ respectively. $\bar{b}$ shows opposite behaviour with $\ell_0$ and $\alpha$. We also find that the deflection angle $\alpha_D$, angular position $\theta_{\infty}$ and $u_{m}$ decrease, but angular separation $s$ increases with $\alpha$. We compare our results with those for Kerr black holes, and also apply the formalism to discuss the astrophysical consequences in the context of the supermassive black holes Sgr A* and M87*. We observe that the deviations of the angular positions from that of the Kerr black hole are not more than $2.6~\mu$as for Sgr A* and $1.96~\mu$as for M87*, which are unlikely to be resolved by the current EHT observations.

Strong gravitational lensing—a probe for extra dimensions and Kalb-Ramond field

Strong field gravitational lensing in the context of both higher spacetime dimensions and in presence of Kalb-Ramond field have been studied. After developing proper analytical tools to analyze the problem we consider gravitational lensing in three distinct black hole spacetimes—(a) four dimensional black hole in presence of Kalb-Ramond field, (b) brane world black holes with Kalb-Ramond field and finally (c) black hole solution in f(T) gravity. In all the three situations we have depicted the behavior of three observables: the asymptotic position approached by the relativistic images, the angular separation and magnitude difference between the outermost images with others packed inner ones, both numerically and analytically. Difference between these scenarios have also been discussed along with possible observational signatures.

Strong field gravitational lensing by a stringy charged black hole

In this paper, we study gravitational lensing of magnetically charged black hole of string theory as a strong field approximation for the supermassive black hole at the center of NGC4486B. We evaluate light deflection angle numerically, from which we obtain magnifications, Einstein rings and observables for the relativistic images. Finally, we explore time delay between relativistic images when they are on the same as well as opposite side of the lens. It is concluded that charge parameter plays a prominent role in the strong gravitational lensing.

Strong field gravitational lensing by a charged Galileon black hole

Strong field gravitational lensings are dramatically disparate from those in the weak field by representing relativistic images due to light winds one to infinity loops around a lens before escaping. We study such a lensing caused by a charged Galileon black hole, which is expected to have possibility to evade no-hair theorem. We calculate the angular separations and time delays between different relativistic images of the charged Galileon black hole. All these observables can potentially be used to discriminate a charged Galileon black hole from others. We estimate the magnitudes of these observables for the closest supermassive black hole Sgr A*. The strong field lensing observables of the charged Galileon black hole can be close to those of a tidal Reissner-Nordström black hole or those of a Reissner-Nordström black hole. It will be helpful to distinguish these black holes if we can separate the outermost relativistic images and determine their angular separation, brightness difference and time delay, although it requires techniques beyond the current limit.

Role of deficit solid angle and quintessence-like matter in strong field gravitational lensing

Using the strong field limit approach, the strong field gravitational lensing in a black hole with deficit solid angle (DSA) and surrounded by quintessence-like matter (QM) has been investigated. The results show that the DSA [Formula: see text], the energy density of QM [Formula: see text] and the equation of state (EOS) parameter [Formula: see text] have some distinct effects on the strong field gravitational lensing. As [Formula: see text] or [Formula: see text] increases, the deflection angle and the strong field limit coefficients all increase faster and faster. Moreover, the evolution of the main observables also has been studied, which shows that the curves at [Formula: see text] are more steepy than those of [Formula: see text]. Compared with the Schwarzschild black hole, the black hole surrounded by QM has smaller relative magnitudes, and at [Formula: see text] both the angular position and angular separation are slightly bigger than those of Schwarzschild black hole, but when [Formula: see text], the angular position and the relative magnitudes all diminish significantly. Therefore, by studying the strong gravitational lensing, we can distinguish the black hole with a DSA and surrounded by QM from the Schwarzschild black hole and the effects of the DSA and QM on the strong gravitational lensing by black holes can be known better.

FAST VARIABILITY AND MILLIMETER/IR FLARES IN GRMHD MODELS OF Sgr A* FROM STRONG-FIELD GRAVITATIONAL LENSING

We explore the variability properties of long, high cadence GRMHD simulations across the electromagnetic spectrum using an efficient, GPU-based radiative transfer algorithm. We focus on both disk- and jet-dominated simulations with parameters that successfully reproduce the time-averaged spectral properties of Sgr A* and the size of its image at 1.3mm. We find that the disk-dominated models produce short timescale variability with amplitudes and power spectra that closely resemble those inferred observationally. In contrast, jet-dominated models generate only slow variability, at lower flux levels. Neither set of models show any X-ray flares, which most likely indicate that additional physics, such as particle acceleration mechanisms, need to be incorporated into the GRMHD simulations to account for them. The disk-dominated models show strong, short-lived mm/IR flares, with short (<~ 1hr) time lags between the mm and IR wavelengths, that arise from strong-field gravitational lensing of magnetic flux tubes near the horizon. Such events provide a natural explanation for the observed IR flares with no X-ray counterparts.

Erratum to: Strong Gravitational Lensing in the Einstein-Proca Theory

In this erratum, we correct and clarify some of statements in our published paper. A few equations given in our paper were actually obtained and published many years ago by Virbhadra’s research group of strong field gravitational lensing. We clarify that those equations were neither obtained by us nor by others cited in our paper. (A) In section.2 on page number 1247 of our paper, we correct our statement: According to the geometric principle, the relationship between the image and the source angular positions is described by the famous Virbhadra-Ellis lens equation [1]. This equation is written in our paper as Eq. (7). tan θ − tan β = DLS / [tan θ + tan(α − α)]×DOS. (1)

Strong field gravitational lensing in stringy black hole

In this paper, we studied the strong gravitational lensing due to the stringy black hole using the strong field limit approach. Modeling the supermassive object at the galactic center as stringy black hole, the numerical values of the strong field limit coefficients and the observables were estimated. Moreover, by measuring the observables, one can get the strong field limit coefficients to reconstruct the full expansion of the deflection angle for the strong field gravitational lensing in stringy black hole. Comparing our results with that of Schwarzschild black hole, it is easy to find that all the values in stringy black hole diverge from those of Schwarzschild spacetime under the influence of the parameter α, which gives us an alternative way to distinguish the stringy black hole from the Schwarzschild black hole. In our model, with the parameter α increasing, the angular position θ ∞ increases and the relative magnitudes $\mathcal{R}_{m}$ decreases.

What does a binary black hole merger look like?

We present a method of calculating the strong-field gravitational lensing caused by many analytic and numerical spacetimes. We use this procedure to calculate the distortion caused by isolated black holes (BHs) and by numerically evolved BH binaries. We produce both demonstrative images illustrating details of the spatial distortion and realistic images of collections of stars taking both lensing amplification and redshift into account. On large scales the lensing from inspiraling binaries resembles that of single BHs, but on small scales the resulting images show complex and in some cases self-similar structure across different angular scales.

Null Geodesics and Strong Field Gravitational Lensing in a String Cloud Background

This paper is devoted to studying two interesting issues of a black hole with string cloud background. Firstly, we investigate null geodesics and find unstable orbital motion of particles. Secondly, we calculate deflection angle in strong field limit. We then find positions, magnifications, and observables of relativistic images for supermassive black hole at the galactic center. We conclude that string parameter highly affects the lensing process and results turn out to be quite different from the Schwarzschild black hole.

Strong gravitational lensing in a black-hole spacetime dominated by dark energy

We study the influence of phantom fields on strong field gravitational lensing. Supposing that the gravitational field of the supermassive central object of the Galaxy is described by a phantom black hole metric, we estimate the numerical values of the coefficients and observations and find that the influence of the phantom fields is somewhat similar to that of the electric charge in a Reissner-Nordstr\"om black hole, i.e., the deflect angle and angular separation increase with the phantom constant $b$. However, other observations are contrary to the Reissner-Nordstr\"om case and show the effects of dark energy, such as (i) compressing the usual black hole and more powerfully attracting photons, (ii) making the relativistic Einstein ring larger than that of the usual black hole, and (iii) not weakening the usual relative magnitudes, which will facilitate observations.

Strong Field Gravitational Lensing in a Magnetic Charged Reissner-Nordström Black Hole Pierced by a Cosmic String

The principal focus of this paper is to study the strong field gravitational lensing in a magnetic charged Reissner-Nordstrom black hole based on the method of cosmic string. We obtain the new coefficients including the tension of the cosmic strings, the strong field deflection limit coefficients, the deflection angle and the magnification, and obtain the relationship between the cosmic string parameter and the new coefficients. The result shows that the cosmic strings have some important effect on the gravitational lensing in a black hole when they pierce it.

Probing spacetime noncommutative constant via charged astrophysical black hole lensing

We study the influence of the spacetime noncommutative parameter on the strong field gravitational lensing in the noncommutative Reissner-Nordstr\"{o}m black-hole spacetime. Supposing that the gravitational field of the supermassive central object of the Galaxy is described by this metric, we estimate the numerical values of the coefficients and observables for strong gravitational lensing. Our results show that with the increase of the parameter $\sqrt{\vartheta}$, the observables $\theta_{\infty}$ and $r_m$ decrease, while $s$ increases. Our results also show that i) if $\sqrt{\vartheta}$ is strong, the observables are close to those of the noncommutative Schwarzschild black hole lensing; ii) if $\sqrt{\vartheta}$ is weak, the observables are close to those of the commutative Reissner-Nordstr\"{o}m black hole lensing; iii) the detectable scope of $\vartheta$ in a noncommutative Reissner-Nordstr\"{o}m black hole lensing is $0.12\leq\sqrt{\vartheta}\leq0.26$, which is wider than that in a noncommutative Schwarzschild black hole lensing, $0.18\leq\sqrt{\vartheta}\leq0.26$. This may offer a way to probe the spacetime noncommutative constant $\vartheta$ by the astronomical instruments in the future.

Strong gravitational lensing in a noncommutative black-hole spacetime

Noncommutative geometry may be a starting point to a quantum gravity. We study the influence of the spacetime noncommutative parameter on the strong field gravitational lensing in the noncommutative Schwarzschild black-hole spacetime and obtain the angular position and magnification of the relativistic images. Supposing that the gravitational field of the supermassive central object of the galaxy described by this metric, we estimate the numerical values of the coefficients and observables for strong gravitational lensing. Comparing to the Reissner-Norstr\"{om} black hole, we find that the influences of the spacetime noncommutative parameter is similar to those of the charge, just these influences are much smaller. This may offer a way to distinguish a noncommutative black hole from a Reissner-Norstr\"{om} black hole, and may probe the spacetime noncommutative constant $\vartheta$ \cite{foot} by the astronomical instruments in the future.

Strong field gravitational lensing in the deformed Hořava-Lifshitz black hole

Adopting the strong field limit approach, we studied the properties of strong field gravitational lensing in the deformed Horava-Lifshitz black hole and obtained the angular position and magnification of the relativistic images. Supposing that the gravitational field of the supermassive central object of the galaxy described by this metric, we estimated the numerical values of the coefficients and observables for gravitational lensing in the strong field limit. Comparing with the Reissner-Nordstroem black hole, we find that with the increase of parameter {alpha}, the angular position {theta}{sub {infinity}} decreases more slowly and r{sub m} more quickly, but angular separation s increases more rapidly. This may offer a way to distinguish a deformed Horava-Lifshitz black hole from a Reissner-Nordstroem black hole by the astronomical instruments in the future.

Rotating brane-world black hole lensing in the strong deflection limit

We consider the metric describing a rotating black hole with tidal charge in the Randall-Sundrum brane world. We study strong field gravitational lensing by this black hole in the quasi-equatorial plane. We compute the angular position of the relativistic caustic points, magnification of the relativistic images and also the critical curves as functions of the metric parameters including the tidal charge. Certain interesting comparisons of the lensing quantities are found with their corresponding properties for the Kerr black hole.

Particle motion and gravitational lensing in the metric of a dilaton black hole in a de Sitter universe

We consider the metric exterior to a charged dilaton black hole in a de Sitter universe. We study the motion of a test particle in this metric. Conserved quantities are identified and the Hamilton-Jacobi method is employed for the solutions of the equations of motion. At large distances from the black hole the Hubble expansion of the universe modifies the effective potential such that bound orbits could exist up to an upper limit of the angular momentum per mass for the orbiting test particle. We then study the phenomenon of strong field gravitational lensing by these black holes by extending the standard formalism of strong lensing to the non-asymptotically flat dilaton-de Sitter metric. Expressions for the various lensing quantities are obtained in terms of the metric coefficients.

Strong field gravitational lensing in scalar–tensor theories

Strong field gravitational lensing in the Brans–Dicke scalar–tensor theory has been studied. The deflection angle for photons passing very close to the photon sphere is estimated for the static spherically symmetric spacetime of the theory and the position and magnification of the relativistic images are obtained. Modelling the super massive central object of the galaxy by the Brans–Dicke spacetime, numerical values of different strong lensing observables are estimated. It is found that against the expectation there is no significant scalar field effect on the strong field observable lensing parameters. This result raises question on the potentiality of strong field lensing to discriminate different gravitational theories.