Tushar Kanti Dey, Surajit Sen
We have investigated the gravitational lensing by two wormholes, viz., Janis-Newman-Winnicour (JNW) wormhole and Ellis wormhole. The deflection angle in the strong field limit is calculated and various lens parameters of two wormholes are compared. It is shown that the JNW wormhole exhibits the relativistic images, while the Ellis wormhole does not have any relativistic images due to the absence of its photon sphere.
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Gravitational lensing by traversable Lorentzian wormholes is a ew possibility which is analyzed here in the strong field limit. Wormhole solutions are considered in the Einstein minimally coupled theory and in the brane world model. The observables in both the theories show significant differences from those arising in the Schwarzschild black hole lensing. As a corollary, it follows that wormholes with zero Keplerian mass exhibit lensing properties which are qualitatively (though not quantitatively) the same as those of a Schwarzschild black hole. Some special features of the considered soluti…
It has been recently shown that Hoyle-Narlikar's C-field theory admits wormhole geometry. We derive the deflection angle of light rays caused by C-field wormhole in the strong field limit approach of gravitational lensing theory. The linearized stability of C-field wormhole under spherically symmetric perturbations about static equilibrium is also explored.
We propose the use of modulated spectra of astronomical sources due to gravitational lensing to probe Ellis wormholes. The modulation factor due to gravitational lensing by the Ellis wormhole is calculated. Within the geometrical optics approximation, the normal point mass lens and the Ellis wormhole are indistinguishable unless we know the source's unlensed luminosity. This degeneracy is resolved with the significant wave effect in the low frequency domain if we take the deviation from the geometrical optics into account. We can roughly estimate the upper bound for the number density of Ellis…
It has been shown that a noncommutative-geometry background may be able to support traversable wormholes. This paper discusses the possible detection of such wormholes in the outer regions of galactic halos by means of gravitational lensing. The procedure allows a comparison to other models such as the Navarro-Frenk-White model and f(R) modified gravity and is likely to favor a model based on noncommutative geometry.
We obtain static multi-polytropic wormhole solutions in the framework of GR gravity. The resulting metric is asymptotically Minkowskian, and locally that of a wormhole. We also examine gravitational lensing by the wormhole, and calculate the deflection angle for weak and strong field limits. We investigate microlensing in the weak field limit and obtain corresponding light curves for both galactic and extragalactic situations. We discuss the multi-polytropic equation of state for the energy-momentum tensor which supports this geometry and finally, we check for the satisfaction of the weak ener…
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…
Natural wormholes and its astrophysical signatures have been sugested in various oportunities. By applying the strong field limit of gravitational lensing theory, we calculate the deflection angle and magnification curves produced by Morris-Thorne wormholes in asimptotically flat space-times. The results show that wormholes act like convergent lenses. Therefore, we show that it is hard to distinguish them from black holes using the deflection's angle of the gravitational lens effect, in contrast with the results reported by Cramer et.al. and Safanova et.al. However, we also show that it is pos…
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 discuss the peculiarities of gravitational lensing by spherically symmetric wormholes if they are not symmetric with respect to their throats. It is noticed, in particular, that wormholes always contain the so-called photon spheres, near which the photon deflection angles can be arbitrarily large, but, in general, the throat is such a sphere only for symmetric wormholes. In some cases, photons from outside can cross the throat and return back from a neighborhood of a photon sphere if the latter is located beyond the throat. Two families of generally asymmetric wormhole configurations are co…
The problem of bending and scattering of light rays passing outside from the entrance to a wormhole with zero gravitational mass is considered. The process of ray capture by a wormhole as well as the process of formation of a shadow when illuminated by a standard screen is investigated. These mechanisms are also compared to the case of motion of light rays in the vicinity of the Schwarzschild black hole.
Gravitational lensing by traversable wormholes supported by three-form fields
本文研究三形式场支撑的可穿越虫洞的引力透镜效应，发现光子球半径是分析虫洞几何结构的有用可观测量。
In this work, we calculate the deflection angle of light in a spacetime that interpolates between regular black holes and traversable wormholes, depending on the free parameter of the metric. Afterwards, this angular deflection is substituted into the lens equations which allows to obtain physically measurable results, such as the position of the relativistic images and the magnifications.
The present paper is intended for studying the effect of strong gravitational lensing in the context of charged wormhole. To study this effect, the conditions determining the existence of photon spheres at and outside the throat are obtained. The necessary and sufficient conditions for the existence of photon spheres at or outside the throat of the charged wormhole is derived. Furthermore, photon spheres are investigated in three cases for three different forms of redshift function. These three cases include the existence of effective photon spheres (i) at the throat, (ii) outside the throat a…
It has been argued that the recently detected ring-down gravity waveforms could be indicative only of the presence of light rings in a horizonless object, such as a surgical Schwarzschild wormhole, with the frequencies differing drastically from those of the horizon quasinormal mode frequencies $ω_{\text{QNM}}$ at late times. While the possibility of such a horizonless alternative is novel by itself, we show by the example of Ellis-Bronnikov wormhole that the differences in $ω_{\text{QNM}}$ in the eikonal limit (large $l$) need not be drastic. This result will be reached by exploiting the conn…
Higher-order correction to weak-field lensing of an Ellis-Bronnikov wormhole
本文研究了 Ellis-Bronnikov 虫洞在弱场近似下精确至 1/b^4 阶的偏折角，比较了多种近似方法的精度并进行了排名，同时指出部分方法对坐标系选择敏感。
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…
A recent study by Rahaman et al. has shown that the galactic halo possesses the necessary properties for supporting traversable wormholes, based on two observational results, the density profile due to Navarro et al. and the observed flat rotation curves of galaxies. Using a method for calculating the deflection angle pioneered by V. Bozza, it is shown that the deflection angle diverges at the throat of the wormhole. The resulting photon sphere has a radius of 0.40 ly. Given the dark-matter background, detection may be possible from past data using ordinary light.
Shadow and strong gravitational lensing of new wormhole solutions supported by embedding Class-I condition
本文提出两类满足 Class-I 嵌入条件的新虫洞解，通过零测地线与数值计算分析其阴影、强偏转及透镜观测量，并指出 r_th=3M 虫洞的 Einstein 环等图像具备探测可能。
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…
Lensing observables: Massless dyonic vis-à-vis Ellis wormhole
本文应用参数化后牛顿方法，比较了无质量双荷虫洞与 Ellis 虫洞的引力透镜观测特征，发现两者定性相似但定量依赖参数，并指出差分时间延迟修正存在意外发散。
Strong field lensing by Damour-Solodukhin wormhole
本文研究 Damour-Solodukhin 虫洞的强场透镜观测，发现偏差参数 $\lambda$ 可在远大于极小值的范围内仍重现黑洞透镜特征，反驳了所有实验需在同一 $\lambda$ 范围模拟黑洞的直觉预期。
Gravitational lensing of the wormhole in the Eddington-inspired Born-Infeld spacetime with a cosmic string
研究EiBI时空中含宇宙弦虫洞的引力透镜，发现宇宙弦增强强场光线偏折，影响像的角分离与亮度，深化对拓扑缺陷虫洞结构的理解。
Gravitational lensing and deflection angles of generalised Ellis-Bronnikov wormhole embedded in a warped braneworld background
研究广义埃利斯-布朗尼科夫虫洞及其在五维扭曲分支世界背景中的引力透镜效应和偏转角，分析不同参数对透镜特性的影响。
Slowly Rotating Wormholes in f(R,T) Gravity: Particle Dynamics and Weak-field Lensing
本研究在f(R,T)引力框架下构建慢速旋转可穿越虫洞模型，证明其无需奇异物质且满足能量条件，并分析了粒子动力学与弱场透镜效应，表明其具有天体物理可行性。
Wormholes are one of the most interesting topological features in spacetime, offering a rat run between two vastly separated regions of the universe. In this paper, we study the deflection angle of light by wormholes, which are supported by electric charge, magnetic charge, and scalar fields in the weak field limit approximation. To this end, we apply new geometric methods -- the Gauss-Bonnet theorem and the optical geometry -- to compute the deflection angles. We also verify our findings by using the well-known geodesics method. There exists a similarity between the charge and the quantum cor…
Traversable Wormholes in Einstein-Euler-Heisenberg Gravity: Geometry, Energy Conditions, and Gravitational Lensing
本研究在爱因斯坦-欧拉-海森堡引力框架下探讨可穿越虫洞，发现量子修正可减少奇异物质需求，并计算了虫洞质量及引力透镜偏转角，表明非线性电动力学修正增强透镜效应。
Horizonless compact objects with light rings (or photon spheres) are becoming increasingly popular in recent years for several reasons. In this paper, we show that a horizonless object such as a wormhole of Morris-Thorne type can have two photon spheres. In particular, we show that, in addition to the one present outside a wormhole throat, the throat can itself act as an effective photon sphere. Such wormholes exhibit two sets of relativistic Einstein ring systems formed due to strong gravitational lensing. We consider a previously obtained wormhole solution as a specific example. If such type…
A new exact vacuum solution in five dimensions, which describes a magnetized cylindrical wormhole in $3+1$ dimensions is presented. The magnetic field lines are stretched along the wormhole throat and are concentrated near to it. We study the motion of neutral and charged test particles under the influence of the magnetized wormhole. The effective potential for a neutral test particle around and across the magnetized wormhole has a repulsive character. The gravitational lensing for the magnetized wormhole for various lens parameters are calculated and compared. The total magnetic flux on eithe…
Gravitational lensing by Lema\^ıtre-Tolman-Bondi wormholes in a Friedmann universe
研究Friedmann宇宙中LTB虫洞的引力透镜效应，发现虫洞阴影角大小随观测时间非单调变化，早期减小、后期因宇宙膨胀而增大。
Image of an accreting general Ellis-Bronnikov wormhole
本文研究广义 Ellis-Bronnikov 虫洞时空中光的传播、阴影及吸积盘图像，并与 Schwarzschild 黑洞图像特征进行比较，为未来超大质量天体观测提供参考。
Gravitational Lensing Phenomena of Ellis-Bronnikov-Morris-Thorne Wormhole with Global Monopole and Cosmic String
本文针对含整体单极子和宇宙弦的Ellis-Bronnikov-Morris-Thorne虫洞，理论研究其引力透镜现象，推导弱场极限下光子偏转角解析表达式，分析相关参数影响及喉半径为零的特殊情况。
Strong gravitational lensing by wormholes
本研究针对静态虫洞的强引力透镜效应展开分析，对比黑洞透镜的差异，探讨观测者与光源在虫洞喉同侧/异侧的情形，揭示光子球相关独特成像特征，为探测奇异虫洞几何提供明确标识。
Gravitational Lensing in a Kasner Background: Distinguishing Wormholes and Black Holes
研究嵌入各向异性比安奇 - I 宇宙学中致密天体的引力透镜效应，用方向雅可比映射推导相关方程和曲线，表明特征尺度分裂可探各向异性膨胀，临界曲线变形弱，且不同弱场偏转定律对相同背景过滤不同，为解开宇宙学各向异性提供框架。
Throat effects on strong gravitational lensing in Kerr-like wormholes
本文研究类Kerr单参数虫洞的强引力透镜，通过分类径向势根并分析喉部形成二重根或三重根的条件，揭示三重根导致的幂律发散及光线穿越喉部的观测特征。
Traversable Wormholes in non-minimal Einstein-Yang-Mills Gravity: Geometry, Energy Conditions, and Gravitational Lensing
本研究在非最小爱因斯坦-杨-米尔斯引力框架下提出一类静态球对称可穿越虫洞解，分析了耦合常数与磁荷对虫洞几何、能量条件的影响，并通过引力透镜研究验证了其引力场的吸引特性，为可穿越虫洞研究提供了新的理论方向。
Gravitational lensing outside and inside of a marginally unstable photon sphere at a $Z_2$-symmetric wormhole throat in strong deflection limits
本文研究Z₂对称虫洞喉处边缘不稳定光子球内外的引力透镜效应，发现其偏折角呈幂次发散，修正了相关幂次发散项系数，得到强偏转极限下该类虫洞偏折角的普适性质。
Can massless wormholes mimic a Schwarzschild black hole in the strong field lensing?
本文研究无质量虫洞能否在强场透镜观测中模拟 Schwarzschild 黑洞，发现 EMS 理论中的无质量虫洞可紧密模拟，而 EMD 理论因膨胀子电荷影响而差异显著。
Distinguishing wormholes via Einstein rings and global curvature
研究嵌入弯曲FLRW宇宙的静态埃利斯 - 布罗尼科夫虫洞引力透镜特性，用曲率相关宇宙学距离推导弱场透镜方程，对比虫洞与黑洞爱因斯坦环半径缩放及透镜信号红移演化来区分两者。
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…
In this paper, we analyze the deflection angle of light by Brane-Dicke wormhole in the weak field limit approximation to find the effect of the Brane-Dicke coupling parameter on the weak gravitation lensing. For this purpose, we consider new geometric techniques, i.e., Gauss-Bonnet theorem and optical geometry in order to calculate the deflection angle. Furthermore, we verify our results by considering the most familiar geodesic technique. Moreover, we establish the quantum corrected metric of Brane-Dicke wormhole by replacing the classical geodesic with Bohmian trajectories, whose matter sour…
EFT Corrections to Photon Propagation and Gravitational Lensing in an Ellis-Bronnikov Wormhole
研究EB虫hole的强引力透镜，推导电磁场与时空曲率非最小耦合的修正光子传播定律，发现特定EFT相互作用可提供区分虫hole与黑洞的独特透镜特征。
In this paper, we study the deflection angle for wormhole-like static aether solution by using Gibbons and Werner technique in non-plasma, plasma, and dark matter mediums. For this purpose, we use optical spacetime geometry to calculate the Gaussian optical curvature, then implement the Gauss-Bonnet theorem in weak field limits. Moreover, we compute the deflection angle by using a technique known as Keeton and Petters technique. Furthermore, we analyze the graphical behavior of the bending angle $ψ$ with respect to the impact parameter $b$, mass $m$ as an integration constant, and parameter $q…
A method to calculate light curves of the gravitational microlensing of the Ellis wormhole is derived in the weak-field limit. In this limit, lensing by the wormhole produces one image outside the Einstein ring and one other image inside. The weak-field hypothesis is a good approximation in Galactic lensing if the throat radius is less than $10^{11} km$. The light curves calculated have gutters of approximately 4% immediately outside the Einstein ring crossing times. The magnification of the Ellis wormhole lensing is generally less than that of Schwarzschild lensing. The optical depths and eve…
We study gravitational lensing by a class of zero Ricci scalar wormholes which arise as solutions in a scalar-tensor theory of gravity. An attempt is made to find a possible link between lensing features, stable/unstable photon orbits and the energy conditions on the matter required to support these spacetimes. Our analysis shows (for this class of wormholes) that light rays always exhibit a positive deflection if the energy conditions are satisfied (nonexotic matter content). In contrast, if the energy conditions are violated (exotic matter), the net deflection of a light ray may be positive,…
Gravitational lensing in a topologically charged Eddington-inspired Born-Infeld spacetime
本文研究拓扑荷磁单极/虫洞在弱场与强场极限下的引力透镜，计算光线偏折并确定观测物理量，发现拓扑荷使观测结果区别于广义相对论虫洞情形。
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…
In this paper, we study the perturbation problem of the scalar, electromagnetic, and gravitational waves under the traversable Lorentzian wormhole geometry. The unified form of the potential for the Schrödinger type one-dimensional wave equation is found.
We consider the Brill metric which is an electrovacuum solution to Einstein's field equation. It depends on three parameters, a mass parameter $m$, a NUT parameter $l$ and a charge parameter $e$. If the charge parameter is small, the metric describes a black hole; if it is sufficiently big, it describes a wormhole. We determine the relevant lensing features both in the black-hole and in the wormhole case. In particular, we give formulas for the photon spheres, for the angular radius of the shadow and for the deflection angle. We illustrate the lensing features with the help of an effective pot…
In this paper, the gravitational wave generation by a slowly rotating thin-shell wormhole is considered. Since the rotating thin-shell wormhole is assumed to be an axisymmetric rigid body, the rotation axis coincides with the largest principal axis which means there is no precession motion. However, if there is a perturbation in the angular velocity, the rotating wormhole can move with precession by perturbation which make arise the gravitational waves. We derive the gravitational wave spectrum, energy loss rate, and angular momentum loss rate.
In this paper, the gravitational deflection of relativistic massive particles up to the second post-Minkowskian order by static and spherically symmetric wormholes is investigated in the weak-field limit. These wormholes include the Janis-Newman-Winicour wormhole, a class of zero Ricci scalar scalar-tensor wormholes, and a class of charged Einstein-Maxwell-dilaton wormholes. With the Jacobi metric approach, the Gauss-Bonnet theorem is employed to study the gravitational deflection. In this scheme, the deflection angle as a topological effect is considered. Moreover, we analyze the influence of…
We consider a class of stationary and axisymmetric wormhole spacetimes that is closely related to, but not identical with, the class of Teo wormholes. We fix a point $p$ (observation event) and a timelike curve $γ$ (worldline of a light source), and we characterize the set of all past-oriented lightlike geodesics from $p$ to $γ$. As any such geodesic corresponds to an image of the light source on the observer's sky, this allows us to investigate the lensing properties of the wormhole. As a main result, we prove with the help of Morse theory that, under very mild conditions on $γ$, the observer…
Finite mass two throat wormholes: global light rings, branch resolved strong lensing, and scalar transmission
该研究引入静态双喉虫洞族，通过四次嵌入轮廓有限质量变形构建模型。解析推导对数强偏转系数，验证标量散射相关结论。此模型能从一个时空导出拓扑、能量条件、强引力透镜及波传输等，提供了有限质量设定。
The gravitational perturbation of the Morris-Thorne wormhole has been derived by using the Newman-Penrose formalism. We apply Teukolsky equation to the wormhole spacetime, compute the perturbed Weyl scalars, $Ψ_{4}^{(1)}$ and obtain its master equation, decomposed in spin weighted spherical harmonics with spin weight $-2$. For simplicity, we consider the perturbation provoked by a single gaussian pulse of pressureless dust matter.
This paper has been withdrawn by the author due to a crucial sign error in equation 1
A traversable wormhole solution of general scalar-tensor field equations is presented. We have shown, after a numerical analysis for the behavior of the scalar field of Brans-Dicke theory, that the solution is completely singularity--free. Furthermore, the analysis of more general scalar field dependent coupling constants indicates that the gravitational memory phenomenon may play an important role in the fate of natural wormholes.
Wormholes that meet the flare-out condition violate the weak energy condition in classical general relativity. The purpose of this note is to show that even a slight modification of the gravitational theory could, under certain conditions, avoid this violation for matter threading the wormhole. The first part discusses some general criteria based on the field equations, while the second part assumes a specific equation of state describing normal matter, together with a particular type of shape function. The analysis is confined to wormholes with zero tidal forces.
In this work we study and compare the features of gravitational entropy near the throat of transversable wormholes formed by exotic matter and wormholes in galactic halos. We have verified that gravitational entropy and entropy density of these wormholes in regions near their throats are indistinguishable for objects of same throat, despite the fact they are described by different metrics and by distinct energy-momentum tensors. We have found that the gravitational entropy density diverges near the throat for both cases, probably due to a non-trivial topology at this point, however allowing th…
In this work we study the problem of linear stability of gravitational perturbations in stationary and spherically symmetric wormholes. For this purpose, we employ the Newman-Penrose formalism which is well-suited for treating gravitational radiation in General Relativity, as well as the geometrical aspect of this theory. With this method we obtain a "master equation" that describes the behavior of gravitational perturbations that are of odd-parity in the Regge-Wheeler gauge. This equation is later applied to a specific class of Morris-Thorne wormholes and also to the metric of an asymptotical…
In the Bogomol'nyi-Prasad-Sommerfield (BPS) limit of Einstein-Yang-Mills-Higgs theory, we construct numerically a non-Abelian wormhole supported by a phantom field. The probe limit is the Yang-Mills-Higgs field in the background of Ellis wormhole when the gravity is switched off. The wormhole solutions possess the Yang-Mills-Higgs hair in the presence of gravity; Thus a branch of hairy wormhole solutions emerge from the Ellis wormhole when the gravitational coupling constant increases. We find that the mass of wormholes and scalar charge of phantom field increase monotonically when the gravita…
In this paper, we use the Gauss Bonnet theorem to obtain the deflection angle by the photons coupled to Weyl tensor in a Schwarzschild black hole and Schwarzschild-like black hole in bumblebee gravity in the weak limit approximation. To do so, we first calculate the corresponding optical metrics, and then we find the Gaussian curvature to use in Gauss-Bonnet theorem, which is first done by Gibbons and Werner. Hence, in the leading order terms we show the deflection angle, that is affected by the coupling between the photon and Weyl tensor, and there is a deviation from the deflecting angle as …
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