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 hole has been studied in plasma as well as non-plasma medium.
We investigate the solutions of Einstein equations such that a hedgehog solution is matched to different exterior or interior solutions via a spherical shell. In the case where both the exterior and the interior regions are hedgehog solutions or one of them is flat, the resulting spherical shell becomes a stringy shell. We also consider more general matchings and see that in this case the shell deviates from its stringy character.
Gravitational lensing and black hole shadows are one of the strongest observational evidences to prove the existence of black holes in the universe. The gravitational lensing arises due to the deflection of light by the gravitational field of a gravitating body such as a black hole. Investigation of the shadow cast by a compact object as well as deflection of light around it may provide the useful information about physical nature of the particular compact object and other related aspects. In this paper, we study the deflection of light by a dual charged stringy black hole spacetime derived in…
We discuss image formation in gravitational lensing systems using wave optics. Applying the Fresnel-Kirchhoff diffraction formula to waves scattered by a gravitational potential of a lens object, we demonstrate how images of source objects are obtained directly from wave functions without using a lens equation for gravitational lensing.
String theory is a promising candidate for a fundamental quantum theory of all interactions including Einstein gravity. Some solutions in string theory can be interpreted as black holes. Using the semi-analytic method and WKB method,the quasinormal modes(QNMs)of 1+1 dimensional black hole in string theory are studied.The QNMs of 1+3 dimensional black hole in string theory are also calculated through numerical approach.The numerical investigation has shown that the late time gravitational oscillation of the black hole under an external perturbaton is dominated by certain QNMs.
We show how our theory of large-scale gravitational quantization explains the large angle gravitational lensing by galaxies without requiring "dark matter". A galaxy is treated as a collective system of billions of stars in each quantization state with each star experiencing an average gravitational environment analogous to that for nucleons in the atomic nucleus. Consequently, each star is in an approximate finite depth square well type of gravitational potential. The "effective potential" is shown to be about ten times greater than the Newtonian gravitational potential, so the gravitational …
Schwarzschild black holes can produce strong gravitational lensing. The relativistic images are produced due to bending of light around the black hole. We propose a model equation to study the strong gravitational lensing. The model equation can well describe the bending angle from a range very close to the photon sphere to the first relativistic image.
Gravitational lensing caused by the gravitational field of massive objects has been studied and acknowledged for a long period of time. In this paper, however, we propose a different mechanism where the bending of light stems from the non-linear interaction of gravitational, electromagnetic and axion waves that creates the high curvature zone in the space-time fabric. The striking distinction in the present study is that in contrast to the convex lensing in the gravitational field of a massive object, hyperbolic nature of the high curvature zone of the background space-time may give rise to co…
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 present three different theoretically foreseen, but unusual, astrophysical situations where the gravitational lens equation ends up being the same, thus producing a degeneracy problem. These situations are (a) the case of gravitational lensing by exotic stresses (matter violating the weak energy condition and thus having a negative mass, particular cases of wormholes solutions can be used as an example), (b) scalar field gravitational lensing (i.e. when considering the appearance of a scalar charge in the lensing scenario), and (c) gravitational lensing in closed universes (with antipodes).…
We found strong similarities between the gravitational lensing and the conventional optical lensing. The similarities imply a graded refractive index description of the light deflection in gravitational field. We got a general approach to this refractive index in a static spherically symmetric gravitational field and obtained its exterior and interior solutions exactly through the general relativity. In weak field case, the two solutions come to a simple unified exponential function of the gravitational potential. With these results, the gravitational lensing can be analyzed in a convenient op…
In low-energy effective string theory, $α'$ corrections involve the coupling of the dilaton field to Gauss-Bonnet term. We assume that the dilaton potential is fine tuned so that the dilaton field may oscillate rapidly for a while around the minimum of its potential but the inflation background is not affected. By numerical method, we find that if the dilaton starts to oscillate at the time of about $\sim 60$ e-folds before the end of inflation, $α^\prime$ correction may bring unusual oscillations to the inflationary gravitational wave spectrum, which might be measurably imprinted in the CMB B…
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.
We analyzed the influence of static gravitational field on the vacuum and proposed the concept of inhomogeneous vacuum. According to the corresponding Fermat's principle in the general relativity, we derived a graded refractive index of vacuum in a static gravitational field. We found that the light deflection in a gravitational field can be calculated correctly with the use of this refractive index and therefore the gravitational lensing can be treated conveniently with the optical method. For illustration, we simulated the imaging of gravitational lensing, figured out the time delay between …
Considering the spacetime around a rotating massif body it is seen that the time of flight of a light ray is different whether it travels on one side of the source or on the other. The difference is proportional to the angular momentum of the body. In the case that a compact rapidly rotating object is the source of a gravitational lensing effect, the contribution coming from the above mentioned gravitational Aharonov-Bohm effect should be added to the other causes of phase difference between light rays coming from different images of the same object.
Adopting the strong field limit approach, we investigated the strong gravitational lensing in a Brane-World black hole, which means that the strong field limit coefficients and the deflection angle in this gravitational field are obtained. With this result, it can be said with certainly that the strong gravitational lensing is related to the metric of gravitational fields closely, the cosmology parameter α and the dark matter parameter \b{eta} come from the Brane-World black hole exerts a great influence on it. Comparing with the Schwarzschild-AdS spacetime and the Schwarzschild-XCMD spacetime…
We study the gravitational lensing in the weak field approximation assuming the presence of a plasma and of a magnetic field around a compact gravitational source. The external magnetic field causes the split of the image, as the counterpart of the Zeeman effect. The magnetic field affects the magnification of images, creating additional components. We also study the time delay of an electromagnetic signal due to the geometry and the gravitational field around the source. We show that the time delay strongly depends on the plasma parameters. Lastly, we consider the effects of the presence of a…
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…
Gravitational waves propagate along null geodesics like light rays in the geometrical optics approximation, and they may have a chance to suffer from gravitational lensing by intervening objects, as is the case for electromagnetic waves. Long wavelength of gravitational waves and compactness of possible sources may enable us to extract information in the interference among the lensed images. We point out that the interference term contains information of relative transverse velocity of the source-lens-observer system, which may be obtained by possible future space-borne gravitational wave dete…
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.
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 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.
Black hole lensing and gravitational waves are, respectively, closely dependent of the property of the lens and radiation source. In this letter, a universal relation between them is established for a rotating black hole acting simultaneously as a lens and a gravitational wave source, in an asymptotically flat spacetime. The relation only relies on the lens geometry and observable, while is independent of the specific nature of the black hole. Therefore, the possible gravitational wave sources could be located with modern astronomical instrument from the side of the lensing without knowing the…
The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature. It includes the basic equations and the relevant techniques for calculating the position, the shape, and the brightness of images in an arbitrary general-relativistic spacetime. It also includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible numb…
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.
The physics associated with spherically symmetric charged black holes is analyzed from the point of view of using weak gravitational lensing as a means for determining the dimensionality of spacetime. In particular, for exact solutions of electro-vac black holes in four and five spacetime dimensions the motion of photons is studied using the equations for the null geodesics and deriving the weak limit bending angles and delays in photon arrival times.
We consider light propagation as a probe of non-metricity in area metric spacetimes, and find a deviation from the standard Etherington relation for linearized area metric Schwarzschild. This is joint work with Frederic P. Schuller (Erlangen University).
Gravitation lensing calculations, which are generally done for light ray, are extended to that for a massive particle. Many interesting results were observed. We discuss the scattering cross section along-with many consequential quantities here. In particular, the case of Schrwarzschild metric was taken as illustration, though the analysis applies to a wide range of cases, such as extended black holes.
We study the optical properties of the Kehagias-Sfetsos (KS) compact objects, characterized by the "Hořava" parameter $ω_{_{KS}}$, in the presence of plasma, considering its homogeneous or power-law density distribution. The strong effects of both "Hořava" parameter $ω_{_{KS}}$ and plasma on the shadow cast by the KS compact objects are demonstrated. Using the weak field approximation, we investigate the gravitational lensing effect. Strong dependence of the deflection angle of the light on both the "Hořava" and plasma parameter is explicitly shown. The magnification of image source due to the…
We first define what we mean by gravitational lensing equations in a general space-time. A set of exact relations are then derived that can be used as the gravitational lens equations in all physical situations. The caveat is that into these equations there must be inserted a function, a two-parameter family of solutions to the eikonal equation, not easily obtained, that codes all the relevant (conformal) space-time information for this lens equation construction. Knowledge of this two-parameter family of solutions replaces knowledge of the solutions to the geodesic equations. The formalism is…
We consider the possible effects of gravitational lensing by globular clusters on gravitational waves from asymmetric neutron stars in our galaxy. In the lensing of gravitational waves, the long wavelength, compared with the usual case of optical lensing, can lead to the geometrical optics approximation being invalid, in which case a wave optical solution is necessary. In general, wave optical solutions can only be obtained numerically. We describe a computational method that is particularly well suited to numerical wave optics. This method enables us to compare the properties of several lens …
An overview is given on those theoretical gravitational lensing results that can be formulated in a spacetime setting, without assuming that the gravitational fields are weak and that the bending angles are small. The first part is devoted to analytical methods considering spacetimes in which the equations for light rays (lightlike geodesics) is completely integrable. This includes spherically symmetric static spacetimes, the Kerr spacetime and plane gravitational waves. The second part is devoted to qualitative methods which give some information on lensing properties without actually solving…
In previous works we have derived a Running Vacuum Model (RVM) for a string Universe, which provides an effective description of the evolution of 4-dimensional string-inspired cosmologies from inflation till the present epoch. In the context of this "stringy RVM" version, it is assumed that the early Universe is characterised by purely gravitational degrees of freedom, from the massless gravitational string multiplet, including the antisymmetric tensor field. The latter plays an important role, since its dual gives rise to a `stiff' gravitational-axion "matter", which in turn couples to the gr…
It has been suggested that energetic photons propagating in vacuo should experience a non-trivial refractive index due to the foamy structure of space-time induced by quantum-gravitational fluctuations. The sensitivity of recent astrophysical observations, particularly of AGN Mk501 by the MAGIC Collaboration, approaches the Planck scale for a refractive index depending linearly on the photon energy. We present here a new derivation of this quantum-gravitational vacuum refraction index, based on a stringy analogue of the interaction of a photon with internal degrees of freedom in a conventional…
Gravitational lensing by gravitational wave is considered. We notice that although final and initial direction of photons coincide, displacement between final and initial trajectories occurs. This displacement is calculated analytically for the plane gravitational wave pulse. Estimations for observations are discussed.
Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe. This review summarises the theory of gravitational lensing, its main current applications and representative results achieved so far. It has two parts. In the first, starting from the equation of geodesic deviation, the equations of thin and extended gravitational lensing are derived. In the second, gravitational lensing by stars and planets, galaxies, galaxy clusters and large-scale structures is discussed and summarised.
We present the first detailed computations of wave optics effects in the gravitational lensing of binary systems. The field is conceptually rich, combining the caustic singularities produced in classical gravitational lensing with quantum (wave) interference effects. New techniques have enabled us to overcome previous barriers to computation. Recent developments in radio astronomy present observational opportunities which, while still futuristic, appear promising.
In this work the space-time geometry of the halo region in spiral galaxies is obtained considering the observed flat galactic rotation curve feature, invoking the Tully-Fisher relation and assuming the presence of cold dark matter in the galaxy. The gravitational lensing analysis is performed treating the so obtained space-time as a gravitational lens. It is found that the aforementioned space-time as the gravitational lens can consistently explain the galaxy-galaxy weak gravitational lensing observations and the lensing observations of the well-known Abell 370 galaxy cluster.
Singularities of caustics appeared in gravitational lensing effect are discussed analytically. Multipole expansion model of lensing object is mainly studied since it is tractable and universal. Our analyses are confirmed by numerical calculations and applied to multiple quasar system of PG1115+080. Consistencies with elliptical lens models are also discussed.
We present a framework for studying gravitational lensing in spherically symmetric spacetimes using 1+1+2 covariant methods. A general formula for the deflection angle is derived and we show how this can be used to recover the standard result for the Schwarzschild spacetime.
We present a framework, based on the null-surface formulation of general relativity, for discussing the dynamics of Fermat potentials for gravitational lensing in a generic situation without approximations of any kind. Additionally, we derive two lens equations: one for the case of thick compact lenses and the other one for lensing by gravitational waves. These equations in principle generalize the astrophysical scheme for lensing by removing the thin-lens approximation while retaining the weak fields.
This thesis contributes to the field of gravitational lensing (GL) and observational cosmology. We discuss the use of gravitational lensing as a tool in search of exotic objects in the Universe. In the next chapter the concordance of an alternative cosmological model with the current gravitational lensing observations is explored and also a non-minimally coupled effective gravity theory that supports non-topological solitonic solutions is considered. In the last chapter we study propagation of light in strong gravitational field. Using geometrical optics approach we show that massless particle…
We revisit a weak gravitational lensing problem by constructing a setup which describes the actual system as accurately as possible and solving the null geodesic equations. Details are given for the case of a Universe driven only by a cosmological constant, Λ, which confirm the conventional results: The conventional lensing analysis is correct as it is, without any need for correction of O(Λ). We also treat the cases of the lensing in generic FRW backgrounds.
We study a deformation of a $2$-graded Poisson algebra where the functions of the phase space variables are complemented by linear functions of parity odd velocities. The deformation is carried by a $2$-form $B$-field and a bivector $Π$, that we consider as gauge fields of the geometric and non-geometric fluxes $H$, $f$, $Q$ and $R$ arising in the context of string theory compactification. The technique used to deform the Poisson brackets is widely known for the point particle interacting with a $U(1)$ gauge field, but not in the case of non-abelian or higher spin fields. The construction is c…
We investigate the strong gravitational lensing in a Kaluza-Klein black hole with squashed horizons. We find the size of the extra dimension imprints in the radius of the photon sphere, the deflection angle, the angular position and magnification of the relativistic images. Supposing that the gravitational field of the supermassive central object of the Galaxy can be described by this metric, we estimated the numerical values of the coefficients and observables for gravitational lensing in the strong field limit.
We investigate the ability of ground based gravitational wave observatories to detect gravitational wave lensing events caused by stellar mass lenses. We show that LIGO and Virgo possess the sensitivities required to detect lenses with masses as small as $\sim 30 M_\odot$ provided that the gravitational wave is observed with a signal-to-noise ratio of $\sim30$. Third generation observatories will allow detection of gravitational wave lenses with masses of $\sim 1 M_\odot$. Finally, we discuss the possibility of lensing by multiple stars, as is the case if the gravitational radiation is passing…
We utilize Moller's and Einstein's energy-momentum complexes in order to explicitly evaluate the energy distributions associated with the two-dimensional "Schwarzschild" and "Reissner-Nordstrom" black hole backgrounds. While Moller's prescription provides meaningful physical results, Einstein's prescription fails to do so in the aforementioned gravitational backgrounds. These results hold for all two-dimensional static black hole geometries. The results obtained within this context are exploited in order Seifert's hypothesis to be investigated.
We consider the Bianchi identity as a field equation for the distortion of the shapes of images produced by weak gravitational lensing. Using the spin coefficient formalism of Newman and Penrose [1962], we show that certain complex components of the Weyl and Ricci curvature tensors are directly related to fundamental observables in weak gravitational lensing. In the case of weak gravitational fields, we then show that the Bianchi identity provides a field equation for the Ricci tensor assuming a known Weyl tensor. From the Bianchi identity, we derive the integral equation for weak lensing pres…
We investigate the strong gravitational lensing for black hole with scalar charge in massive gravity. We find that the scalar charge and the type of the black hole significantly affect the radius of the photon sphere, deflection angle, angular image position, angular image separation, relative magnifications and time delay in strong gravitational lensing. Our results can be reduced to that of the Schwarzschild and Reissner-Nordstr$\ddot{o}$m black holes in some special cases.
In this paper we investigate the strong gravitational lensing in a charged squashed Kaluza-Klein black hole. We suppose that the supermassive black hole in the galaxy center can be considered by a charged squashed Kaluza-Klein black hole and then we study the strong gravitational lensing theory and estimate the numerical values for parameters and observables of it. We explore the effects of the scale of extra dimension $ρ_0$ and the charge of black hole $ρ_q$ on these parameters and observables.
We investigate the effect of the redshift drift in strong gravitational lensing. The redshift drift produces a time variation of $i)$ the apparent position of a lensed source and $ii)$ the time delay among incoming signals from different images. We dub these effects as angular drift and time delay drift, respectively, and analyze their relevance in cosmology.
We consider hairy black hole solutions of Einstein-Yang-Mills-Dilaton theory, coupled to a Gauss-Bonnet curvature term, and we study their stability under small, spacetime-dependent perturbations. We demonstrate that the stringy corrections do not remove the sphaleronic instabilities of the coloured black holes with the number of unstable modes being equal to the number of nodes of the background gauge function. In the gravitational sector, and in the limit of an infinitely large horizon, the coloured black holes are also found to be unstable. Similar behaviour is exhibited by the magnetically…
Current sky surveys have been conducted very accurately in order to understand our universe. One of the phenomena survey maps provide is gravitational effect. Albert Einstein (1936) first discussed the possibilities of gravitational lensing effects based on his theory of general relativity, which might give us some information about cosmology. We often categorize the effects by micro, weak, and strong lensing types. This paper focuses on the strong gravitational lensing, especially the double-source plane lens systems. It was recently recognized that the double lensing events can provide us wi…
We discuss how small-scale density perturbations on the Fresnel scale affect amplitudes and phases of gravitational waves that are magnified by gravitational lensing in geometric optics. We derive equations that connect the small-scale density perturbations with the amplitude and phase fluctuations to show that such perturbative wave optics effects are significantly boosted in the presence of macro model magnifications such that amplitude and phase fluctuations can easily be observed for highly magnified gravitational waves. We discuss expected signals due to microlensing by stars, dark matter…
We consider binary black holes (BBHs) in a hierarchical triple system where a more compact, less-massive binary is emitting detectable gravitational waves (GWs), and the tertiary is a supermassive BH at the center of a nuclear star cluster. As previous works have shown, the orbital motion of the outer binary can generate a detectable relativistic Doppler boost of the GWs emitted by the orbiting inner binary. We show here that for outer-binary orbits with a period of order one year, there can be a non-negligible probability for repeated gravitational lensing of the GWs emitted by the inner bina…
The amplification of a light beam due to intervening gravitational waves is studied. The previous Jordan frame result according to which the amplification is many orders of magnitude larger in scalar-tensor gravity than in general relativity does not hold in the Einstein conformal frame. Lensing by gravitational waves is discussed in relation to the ongoing and proposed VLBI observations aimed at detecting the scintillation effect.
The effect of gravitational lensing on cosmic microwave background (CMB) anisotropies is investigated using the power spectrum approach. The lensing effect can be calculated in any cosmological model by specifying the evolution of gravitational potential. Previous work on this subject is generalized to a non-flat universe and to a nonlinear evolution regime. Gravitational lensing cannot change the gross distribution of CMB anisotropies, but it may redistribute the power and smooth the sharp features in the CMB power spectrum. The magnitude of this effect is estimated using observational constr…
