The purpose of the current Letter is to give some relations between gravitational lensing in the strong-deflection limit and the frequencies of the quasinormal modes of spherically symmetric, asymptotically flat black holes. On the one side, the obtained relations can give a physical interpretation of the strong-deflection limit parameters. On the other side, they also give an alternative method for the measurement of the frequencies of the quasinormal modes of spherically symmetric, asymptotically flat black holes. They could be applied to the localization of the sources of gravitational waves and could tell us what frequencies of the gravitational waves we could expect from a black hole acting simultaneously as a gravitational lens and a source of gravitational waves.
In this paper, we consider black holes in the consistent Aoki-Gorji-Mukohyama theory of the four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity in the presence of Born-Infeld (BI) nonlinear electrodynamics. We study several optical features of these black holes such as the shadow radius, energy emission rate and deflection angle, and analyse the effect of the coupling constants, the electric charge and cosmological constant on the considered optical quantities. Furthermore, we also employ the connection between the shadow radius and quasinormal modes (QNMs) and investigate small scalar per…
We examine in a semiclassical framework the deflection function of strong gravitational lensing, for static and spherically symmetric black holes, endowed with a photon sphere. From a first-order WKB analysis near the maximum of the Regge-Wheeler potential, we extract the real phase shifts from the S-matrix elements and then we derive the associated semiclassical deflection function, characterized by a logarithmic divergent behavior. More precisely, using the complex angular momentum techniques, we show that the Regge poles and the associated greybody factor residues, for a massless scalar fie…
The impact of an antisymmetric tensor on charged black holes: evaporation process, geodesics, deflection angle, scattering effects and quasinormal modes
Observations of gravitational lenses in strong gravitational fields give us a clue to understanding dark compact objects. In this paper, we extend a method to obtain a deflection angle in a strong deflection limit provided by Bozza [Phys. Rev. D 66, 103001 (2002)] to apply to ultrastatic spacetimes. We also discuss on the order of an error term in the deflection angle. Using the improved method, we consider gravitational lensing by an Ellis wormhole, which is an ultrastatic wormhole of the Morris-Thorne class.
We examine a class of charged black holes in scalar-tensor gravity as gravitational lenses. We find the deflection angle in the strong deflection limit, from which we obtain the positions and the magnifications of the relativistic images. We compare our results with those corresponding to the Reissner-Norstrom spacetime and we analyze the observational aspects in the case of the Galactic supermassive black hole.
A charged black hole was predicted by the Einstein--Horndeski--Maxwell theory. In order to provide its observational signatures, we investigate its weak and strong deflection gravitational lensings. We find its weak deflection lensing observables, including the positions, magnifications and differential time delay of the lensed images. We also obtain its strong deflection lensing observables, including the apparent radius of the photon sphere as well as the angular separation, brightness difference and differential time delay between the relativistic images. Taking the supermassive black hole …
A modified Hayward black hole is a nonsingular black hole. It is proposed to form when the pressure generated by quantum gravity can stop matter's collapse as the matter reaches Planck density. Strong deflection gravitational lensing happening nearby its event horizon might provide some clues of these quantum effects in its central core. We investigate observables of the strong deflection lensing, including angular separations, brightness differences and time delays between its relativistic images, and estimate their values for the supermassive black hole in the Galactic center. We find that i…
Gravitational lensing in the weak field limit, quasinormal spectra, and gray-body factors are investigated in the Reissner-Nordström spacetime corrected by bounce parameters. Using the Gauss-Bonnet theorem, we analyze the effects of bounce corrections to the weak gravitational deflection angle and find that the divergence of the deflection angle can be suppressed by a bounce correction in the Reissner-Nordström spacetime. We also notice that the bounce correction plays the same role as the Morse potential in the deflection angle. Moreover, we derive the perturbation equations with the spin-dep…
In this paper we apply the strong deflection limit approach to investigate the gravitational lensing phenomena beyond general relativity. This is accomplished by considering the lensing effects related to black hole solutions that emerge out of the domain of Einstein gravity, namely, the ones acquired from the method of geometric deformation and the Casadio-Fabbri-Mazzacurati brane-world black holes. The lensing observables, for those brane-world black hole metrics, are compared with the standard ones for the Schwarzschild case. We prove that brane-world black holes could have significantly di…
We consider gravitational lensing under a weak-field approximation and in a strong deflection limit by a Bronnikov-Kim wormhole with the same metric as the one of a wormhole which has been suggested in Einstein-Dirac-Maxwell theory. The metric approaches into the metric of an extreme charged Reissner-Nordström black hole in a black hole limit and it becomes the metric of an spatial Schwarzschild wormhole in an ultrastatic limit. In both of the black hole limit and the ultrastatic limit, the coefficient of a divergent term and the constant term of the deflection angle of a light in the strong d…
In this work are reviewed several aspects of gravitational lensing produced by astrophysical bodies that strongly curve the spacetime in their vicinity. When an object with a photon sphere (e.g. a black hole) is interposed between a source and an observer, in addition to primary and secondary images due to small deflections of the light rays, there are two infinite sets of images called relativistic, produced by light passing close to the photon sphere, which undergoes a large deflection. The positions and magnifications of relativistic images can be obtained numerically or analytically, in th…
In this paper, we discuss the effects of nonlinear electrodynamics (NED) on non-rotating black holes, parametrized by the field coupling parameter $β$ and magnetic charge parameter $P$ in detail. Particularly, we survey physical properties of the magnetically charged black hole, thermodynamic properties, observational appearance, quasinormal modes and absorption cross sections. We then show that the black hole gets colder with increasing charge. Investigating the heat capacity, we see that the black hole is thermally stable, which is amplified by introduction of a generalized uncertainty princ…
In this paper, we study the deflection of light by a class of phantom black hole and wormhole solutions in the weak limit approximation. More specifically, in the first part of this work, we study the deflection of light by Garfinkle-Horowitz-Ströminger black hole and Einstein-Maxwell anti-dilaton black hole using the optical geometry and the Gauss-Bonnet theorem. Our calculations show that gravitational lensing is affected by the phantom scalar field (phantom dilaton). In the second part of this work, we explore the deflection of light by a class of asymptotically flat phantom wormholes. In p…
A Simpson-Visser spacetime has two nonnegative parameters $a$ and $m$ and its metric is correspond with (i) a Schwarzschild metric for $a=0$ and $m\neq0$, (ii) a regular black hole metric for $a<2m$, (iii) a one-way traversable wormhole metric for $a=2m$, (vi) a two-way traversable wormhole metric for $a>2m$, and (v) an Ellis-Bronnikov wormhole metric for $a\neq0$ and $m=0$. The spacetime is one of the most useful spacetimes for the purpose of comprehensively understanding gravitational lensing of light rays reflected by a photon sphere of black holes and wormholes. We have investigated gravit…
Gravitational lensing and deflection angles of generalised Ellis-Bronnikov wormhole embedded in a warped braneworld background
Sitananda College（西坦安达学院）；Indian Institute of Technology, Kharagpur（印度理工学院卡拉格普尔分校）；Dr. Bhawar Singh Porte Govt. PG College（德拉·巴瓦尔·辛格·波特政府研究生学院）；Birla Institute of Technology, Ranchi（比尔拉理工学院兰契分校）
We investigate gravitational lensing by a photon sphere in a Reissner-Nordström naked singularity spacetime in strong deflection limits. Because of the nonexistence of an event horizon and the existence of a potential barrier near an antiphoton sphere, infinite numbers of images slightly inside and outside of a photon sphere can appear. We obtain the analytic expressions of the factors of logarithmic divergent terms and the constant terms of the deflection angles in the strong deflection limits not only the for the little outside but also the barely inside of the photon sphere without Taylor e…
Spin of a test particle is a fundamental property that can affect its motion in a gravitational field. In this work we consider the effect of particle spin on its deflection angle and gravitational lensing in the equatorial plane of arbitrary stationary and axisymmetric spacetimes. To do this we developed a perturbative method that can be applied to spinning signals with arbitrary asymptotic velocity and takes into account the finite distance effect of the source and the observer. The deflection angle $Δφ$ and total travel time $Δt$ are expressed as (quasi-)power series whose coefficients are …
In this paper, using the recent method proposed by Ono, Ishihara and Asada (OIA) who extend the idea of Gibbons and Werner to the stationary and axisymmetric case, we apply the Gauss-Bonnet theorem to the optical metric of the non-rotating and rotating Damour-Solodukhin wormholes spacetimes to study the weak gravitational lensing by these objects. Furthermore, we study the strong gravitational lensing by the non-rotating Damour-Solodukhin wormholes using the Bozza's method to see the differences between the weak lensing and the strong lensing. We demonstrate the relation between the strong def…
The influence of plasma on different effects of gravitational lensing is reviewed. Using the Hamiltonian approach for geometrical optics in a medium in the presence of gravity, an exact formula for the photon deflection angle by a black hole (or another body with a Schwarzschild metric) embedded in plasma with a spherically symmetric density distribution is derived. The deflection angle in this case is determined by the mutual combination of different factors: gravity, dispersion, and refraction. While the effects of deflection by the gravity in vacuum and the refractive deflection in a nonhom…
We apply the Gauss-Bonnet theorem to the study of light rays in a plasma medium in a static and spherically symmetric gravitational field and also to the study of timelike geodesics followed for test massive particles in a spacetime with the same symmetries. The possibility of using the theorem follows from a correspondence between timelike curves followed by light rays in a plasma medium and spatial geodesics in an associated Riemannian optical metric. A similar correspondence follows for massive particles. For some examples and applications, we compute the deflection angle in weak gravitatio…
In this work we extend the approach used in [Emanuel Gallo and Osvaldo M. Moreschi, Phys. Rev. D 83, 12 083007 (2011)] to the study of weak gravitational lensing in a plasma medium. First, we present expressions for the deflection angle and optical scalars in terms of the components of the energy-momentum tensor for spherically symmetric lenses surrounded by a cold non-magnetized plasma. Second, we show that the same expressions can be deduced using the Gauss-Bonnet theorem. Finally, we establish a correspondence between the spatial orbits of photons in a non-homogeneous plasma and the non-geo…
Off-equatorial deflections and gravitational lensing. II. In general stationary and axisymmetric spacetimes
School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院）；Department of Astronomy & MOE Key Laboratory of Artificial Micro- and Nano-structures, School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院天文学系及教育部人工微纳结构重点实验室）
In this work we study the deflection angle $Δφ$ and gravitational lensing of both lightlike and timelike neutral rays in Reissner-Nordström (RN) spacetimes. The exact deflection angle is found as an elliptical function of the impact parameter $b$ and velocity $v$ of the ray, and the charge $Q$ of the spacetime. In obtaining this angle, we found the critical impact parameter $b_c$ and radius of particle sphere $r_c$ that are also dependent on $v$ and $Q$. In general, both the increase of velocity and charge reduces the $b_c$ as well as $r_c$. To study the effect of $v$ and $Q$ on the deflection…
In this paper we study gravitational lensing by STU black holes. We considered extremal limit of two special cases of zero-charged and one-charged black holes, and obtain the deflection angle. We find that the black hole charge increases the deflection angle.
The deflection and gravitational lensing of light and massive particles in arbitrary static, spherically symmetric and asymptotically (anti-)de Sitter spacetimes are considered in this work. We first proved that for spacetimes whose metric satisfying certain conditions, the deflection of null rays with fixed closest distance will not depend on the cosmological constant $Λ$, while that of timelike signals and the apparent angle in gravitational lensing still depend on $Λ$. A two-step perturbative method is then developed to compute the change of the angular coordinate and total travel time in t…
Accretion, greybody factor, quasinormal modes, power spectrum, sparsity of Hawking radiation, and weak gravitational lensing of a minimum measurable length inspired Schwarzchild black hole
We calculate the deflection angle of light from a distant source by a galaxy cluster in Weyl's conformal gravity. The general method of calculation is first applied to calculate the deflection angle in Schwarzschild-de Sitter (Kottler) spacetime. The deflection angle calculated in Kottler spacetime includes the contribution of the cosmological constant, which quantitatively agrees with one work and disagrees with many works in the literature. We then calculate the deflection angle in Mannheim-Kazanas spacetime in two conformally related coordinate systems and find that the result includes cont…
The trajectory deflection and gravitational-electromagnetic dual lensing (GEL) of charged signal in general charged static and spherically symmetric spacetimes are considered in this work. We showed that the perturbative approach previously developed for neutral particles can be extended to the electromagnetic interaction case. The deflection angle still takes a (quasi-)series form and the finite distance effect of both the source and observer can be taken into account. Comparing to pure gravitational case, the apparent angles of the images in the GEL, their magnifications and time delay all r…
In this paper we investigate the strong gravitational lensing with Gauss-Bonnet gravity. By considering the logarithmic term for deflection angle, we obtain the deflection angle $\hatα$ and corresponding parameters $\bar{a}$ and $\bar{b}$. Finally, by using the relations between the observables and lensing parameters, we estimate the observables such as, $θ_{\infty}$, $s$ and $r_m$, for the relativistic images in the Gauss-Bonnet background.
We investigate gravitational lensing by a primary photon sphere which is a sphere filled with unstable circular light orbits, and by a secondary photon sphere on a wormhole throat in a black-bounce spacetime which is suggested in [F. S. N. Lobo, M. E. Rodrigues, M. V. d. S. Silva, A. Simpson, and M. Visser, Phys. Rev. D 103, 084052 (2021)] in strong deflection limits. There is an antiphoton sphere between the primary photon sphere and the secondary photon sphere. If a light source and an observer are on the same side of the wormhole throat, in addition to an infinite number of images slightly …
In this paper the deflection angle of light by a rotating Teo wormhole spacetime is calculated in the weak limit approximation. We mainly focus on the weak deflection angle by revealing the gravitational lensing as a partially global topological effect. We apply the Gauss-Bonnet theorem (GBT) to the optical geometry osculating the Teo-Randers wormhole optical geometry to calculate the deflection angle. Furthermore we find the same result using the standard geodesic method. We have found that the deflection angle can be written as a sum of two terms, namely the first term is proportional to the…
In this paper, we discuss the weak gravitational lensing in the context of stringy black holes. Initially, we examine the deflection angle of photon by charged stringy black hole. For this desire, we compute the Gaussian optical curvature and implement the Gauss-Bonnet theorem to investigate the deflection angle for spherically balanced spacetime of stringy black hole. We also analyze the influence of plasma medium in the weak gravitational lensing for stringy black hole. Moreover, the graphical impact of impact parameter $b$ , black hole charge $Q$ on deflection angle by charged stringy black…
Motivated by recent work on the Modified Maxwell (ModMax) black holes [Phys.Lett.B 10.1016/j.physletb.2020.136011], which are invariant in duality rotations and conformal transformations founded in [ Phys.Rev.D 10.1103/PhysRevD.102.121703], we probe its effects on the shadow cast, weak field gravitational lensing, and neutrino propagation in its vicinity. Using the EHT data for the shadow diameter of Sgr. A* and M87*, and LIGO/VIRGO experiments for the dyonic ModMax black hole perturbations, we find constraints for ModMax parameters such as $Q_\text{m}$ and the screening factor $γ$. We also an…
A First-Order Eikonal Framework for Quasinormal Modes, Shadows, Strong Lensing, and Grey-Body Factors in a Scalarized Black-Hole Metric
University of Hradec Králové（赫拉德茨克拉洛韦大学）；National University of Uzbekistan（乌兹别克斯坦国立大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Tashkent State Technical University（塔什干国立技术大学）；New Uzbekistan University（新乌兹别克斯坦大学）；Tashkent International University of Education（塔什干国际教育大学）；Kimyo International University in Tashkent（塔什干基莫国际大学）；Mamun University（马蒙大学）
Using a new geometrical approach introduced by Gibbons and Werner we study the deflection angle by Reissner-Nordström black holes in the background spacetimes with a global monopole and a cosmic string. By calculating the corresponding optical Gaussian curvature and applying the Gauss-Bonnet theorem to the optical metric we find the leading terms of the deflection angle in the weak limit approximation. We find that the deflection angle increases due to the presence of topological defects.
In this article, we analyze the weak gravitational lensing in the context of Einstein-non-linear Maxwell-Yukawa black hole. To this desire, we derive the deflection angle of light by Einstein-non-linear Maxwell-Yukawa black hole using the Gibbons and Werner method. For this purpose, we obtain the Gaussian curvature and apply the Gauss-Bonnet theorem to find the deflection angle of Einstein-non-linear Maxwell-Yukawa black hole in weak field limits. Moreover, we derive the deflection angle of light in the influence of plasma medium. We also analyze the graphical behavior of deflection angle by E…
Gravitational lensing inside and outside of a marginally unstable photon sphere in a general, static, spherically symmetric, and asymptotically-flat spacetime in strong deflection limits
In this work we study the deflection and gravitational lensing of null and timelike signals in the Kiselev spacetime in the weak field limit, to investigate the effects of the equation of state parameter $ω$ and the matter amount parameter $α$. In doing this, we extend a perturbative method previously developed for asymptotically flat spacetimes whose metric functions have integer-power asymptotic expansions to the case that may or may not be asymptotically flat but with non-integer power expansions. It is found that in the asymptotically flat case ($-1/3<ω<0$) the deflection angles are expres…
In this article, we demonstrate the weak gravitational lensing in the context of Bocharova-Bronnikov-Melnikov-Bekenstein (BBMB) black hole. To this desire, we derive the deflection angle of light in a plasma medium by BBMB black hole using the Gibbons and Werner method. First, we obtain the Gaussian optical curvature and implement the Gauss-Bonnet theorem to investigate the deflection angle for spherically symmetric spacetime of BBMB black hole. Moreover, we also analyze the graphical behavior of deflection angle by BBMB black hole in the presence of plasma medium.
