Characteristic Features of Gravitational Wave Lensing as Probe of Lens Mass Model

To recognize gravitational wave lensing events and being able to differentiate between similar lens models will be of crucial importance once one will be observing several lensing events of gravitational waves per year. In this work, the lensing of gravitational waves is studied in the context of LISA sources and wave-optics regime. While different papers before the studied microlensing effects enhanced by simultaneous strong lensing, the focus is on frequency (time) dependent phase effects produced by one lens that will be visible with only one lensed signal. It is shows how, in the interference regime (i.e., when interference patterns are present in the lensed image), one is able to i) distinguish a lensed waveform from an unlensed one, and ii) differentiate between different lens models. In pure wave-optics, on the other hand, the feasibility of the study depends on the signal-to-noise ratio of the signal and/or the amplitude of the lensing effect. To achieve these goals, the phase of the amplification factor of the different lens models and its effect on the unlensed waveform is studied, and the signal-to-noise calculation to provide some quantitative examples is exploited.     

Deflection in higher-order gravitational lensing

The deflection of light rays by rotating gravitational lens is considered in the framework of higher-order gravitational theory. The bending angle of light is derived. The effect of the massive scalar and tensor components of higher-order gravitational field as well as the gravito-magnetic on light deflection are discussed.     

Using gravitational lenses to detect gravitational waves

Gravitational lenses could be used to detect gravitational waves, because a gravitational wave affects the travel-time of a light ray. In a gravitational lens, this effect produces time-delays between the different images. Thus the bending of light, which was the first experimental confirmation of Einstein's theory, can be used to search for gravitational waves, which are the most poorly confirmed aspect of that same theory. Applying this method to the gravitational lens 0957+561 gives new upper bounds on the amplitude of low-frequency gravitational waves in the universe, and new limits on the energy-density during an early inflationary phase.This Essay received the First Award from the Gravity Research Foundation, 1990-Ed.     

Chiral self-gravitating cosmic vortices

In the framework of general relativity, an exact axisymmetric (vortex) solution of the equations of motion is obtained for the SU(2) symmetric sigma model. This solution is characterized by the topological charge (winding number) and angular deficit. In the linearized approximation, the Lyapunov stability of vortices is proved and the deflection angle of a light ray in the gravitational field of the vortex (gravitational lens effect) is calculated.     

Global Properties of Gravitational Lens Maps¶in a Lorentzian Manifold Setting

In a general-relativistic spacetime (Lorentzian manifold), gravitational lensing can be characterized by a lens map, in analogy to the lens map of the quasi-Newtonian approximation formalism. The lens map is defined on the celestial sphere of the observer (or on part of it) and it takes values in a two-dimensional manifold representing a two-parameter family of worldlines. In this article we use methods from differential topology to characterize global properties of the lens map. Among other things, we use the mapping degree (also known as Brouwer degree) of the lens map as a tool for characterizing the number of images in gravitational lensing situations. Finally, we illustrate the general results with gravitational lensing (a) by a static string, (b) by a spherically symmetric body, (c) in asymptotically simple and empty spacetimes, and (d) in weakly perturbed Robertson–Walker spacetimes. Received: 16 October 2000 / Accepted: 18 January 2001     

Relativistic motion of a free particle in a uniform gravitational field

The problem of the motion of a free particle in a uniform gravitational field is considered. A relativistic solution based on the assumption that the motion is a consequence of the curvature of spacetime is obtained. The results are compared with various results based on the assumption that spacetime is flat in a region in which the gravitational field is uniform. In the curved spacetime approach, if a particle is projected from a point in a uniform gravitational field, the vertical distance covered by the particle in infinite coordinate time is infinite, but the horizontal distance covered and the elapsed proper time of the particle are finite. If spacetime is assumed to be flat and the gravitational motion of a particle a consequence of a relativistic force proportional to the relative mass of the particle, then the results obtained for the motion of a particle in a uniform gravitational field are close to the curved spacetime results. All other assumptions, including the assumption that the motion of a particle in a uniform gravitational field is equivalent to the motion of a particle in a uniformly accelerating frame of reference, lead to results in serious disagreement with the curved spacetime results.     

Dynamical properties of superconducting cosmic strings: (II). Heavy closed strings in magnetic field

We discuss a circular static superconducting cosmic string in a homogeneous magnetic field and show that the mass is independent of the radius provided we choose a GUT scale as well as a reasonable value for the intergalactic magnetic field. A conservative estimate gives a mass of order 10¹⁶ M_⊙. We also discuss various gravitational effects related to this string. The most striking effect is the gravitational lens effect that can produce four images.     

Gravitational model of the string

It is shown that an infinite gravitational flux tube solution in 5D Kaluza‐Klein gravity with the cross section in the Planck region after 5D ? 4D reduction and isometrical embedding in a Minkowski spacetime can be considered as a moving infinite string‐like object. Such an object carries an electric and a magnetic flux. The 4D gravitational waves on the tube are considered.     

Spherically Symmetric Wormhole Gravitational Lens Deflection Angle Signifying Braneworld Cosmology

Previously, the gravitational lens of a wormhole was introduced by various researchers. Their treatment was focused basically on the lens signature that describes wormhole geometrical character such as the differences from a black hole or between any various types of wormhole models. The braneworld scenario provides the idea of spacetime with underlying extra-dimensions. The inclusion of extra-dimensional terms in the lens object spacetime line element will result in some variation in the expression for its gravitational lens deflection angle.Thus in this paper we investigate such variation by deriving this deflection angle expression. As such, this paper not only shows the existence of such variation but also suggests the potential utilization of gravitational lensing to prove the existence of extra dimensions by studying the deflection angle characteristic in accordance with the spacetime expansion rate of the universe.     

A new method to test the cosmic distance duality relation using the strongly lensed gravitational waves

We propose a new method to test the cosmic distance duality relation using the strongly lensed gravitational waves. The simultaneous observation of the image positions, relative time delay between different images, redshift measurements of the lens and the source, together with the mass modelling of the lens galaxy, provide the angular diameter distance to the gravitational wave source. On the other hand, the luminosity distance to the source can be obtained from the observation of the gravitational wave signals. To our knowledge this is the first time a method is proposed to simultaneously measure the angular diameter distance and the luminosity distance from the same source. Hence, the strongly lensed gravitational waves provide a unique method to test the cosmic distance duality relation. With the construction of the third generation gravitational detectors such as the Einstein Telescope, it will be possible to test the cosmic distance duality relation with an accuracy of a few percent.     

Dynamical Effect of Electromagnetic Wave in Spherical Symmetrical Finsler Spacetime

In this paper, the dynamical effect of electromagnetic wave is researched in spherical symmetrical Finsler spacetime. The results show that the effect of tangent vector, which can be determined by the angular momentum and energy of observed particles, can’t change the gravitational lens, but can influence the radar echo delay in spherical symmetrical Finsler spacetime. On the other hand, we also use the first order WKB method to study the electromagnetic perturbation with tangent vector effect of Finsler black hole.     

Analysis of lateral-spread photorefractive planar lenses

The photorefractive planar lens for converting a vertical incident plane wave to a lateral-spread spherical wave and vice versa, is suggested. Using the two-beam coupled-wave theory, the coupled wave equations are derived and their half-analytical solutions are also given in terms of an infinite series. The diffraction properties (beam profiles, diffraction efficiency) of the local volume grating in the lens are presented. And the focusing property of the lens is discussed and compared with that of an ideal convergent spherical wave. It is demonstrated that the suggested photorefractive planar lens shows a good focusing effect.     

On modeling galaxy-scale strong lens systems

I review methods for modeling gravitational lens systems comprising multiple images of a background source surrounding a foreground galaxy. In a Bayesian framework, the likelihood is driven by the nature of the data, which in turn depends on whether the source is point-like or extended. The prior encodes astrophysical expectations about lens galaxy mass distributions, either through a careful choice of model families, or through an explicit Bayesian prior applied to under-constrained free-form models. We can think about different lens modeling methods in terms of their choices of likelihoods and priors.     

New class of N-dimensional braneworlds

The new class of the non-stationary solutions to the system of N-dimensional equations for coupled gravitational and massless scalar field is found. The model represents a single (N-1)-brane in a space-time with one large (infinite) and (N-5) small (compact) space-like extra dimensions. In some particular cases the model corresponds to the gravitational and scalar field standing waves bounded by the brane. These braneworlds can be relevant in string and other higher dimensional models.     

Gravitational Microlensing by Ellis Wormhole: Second Order Effects

Gravitational lensing is the effect of light bending in a gravitational field. It can be used as a possible observational method to detect or exclude the existence of wormholes. In this work, we extend the work by Abe on gravitational microlensing by Ellis wormhole by including the second order deflection term. Using the lens equation and definition of Einstein radius, we find the angular locations of the physical image inside and outside Einstein ring. The work contains a comparative analysis of light curves between the Schwarzschild black hole and the Ellis wormhole that can be used to distinguish such objects though such distinctions are too minute to be observable even in the near future. We also tabulate the optical depth and event rate for lensing by bulge and Large Magellanic Cloud (LMC) stars.     

Regular Magnetic Black Hole Gravitational Lensing

The Bronnikov regular magnetic black hole as a gravitational lens is studied. In nonlinear electrodynamics,photons do not follow null geodesics of background geometry; but move along null geodesics of a corresponding effective geometry. To study the Bronnikov regular magnetic black hole gravitational lensing in the strong deflection limit, the corresponding effective geometry should be obtained firstly. This is the most important and key step. We obtain the deflection angle in the strong deflection limit, and further calculate the angular positions and magnifications of relativistic images as well as the time delay between different relativistic images. The influence of the magnetic charge on the black hole gravitational lensing is also discussed.     

Suspended Particles and the Gravitational Instability of Rotating Magnetised Medium

The effect of uniform rotation on the self gravitational instability of an infinite homogeneous magnetised gas particle medium in the presence of suspended particles is investigated. The equations of the problem are linearized and the general dispersion relation for such system is obtained. The rotation is assumed along two different directions and separate dispersion relation for each case is obtained. The dispersion relation for propagation parallel and perpendicular to the uniform magnetic field along with rotation is derived. The effect of suspended particles on the different modes of propagation is investigated. It is found that in presence of suspended particles, magnetic field, rotation and viscosity, Jeans' criterion determines the condition of gravitational instability of gas-particle medium.     

Faraday rotation due to quadratic gravitation

The linearized field equations of quadratic gravitation in stationary space-time are written in quasi-Maxwell form. The rotation of the polarization plane for an electromagnetic wave propagating in the gravito-electromagnetic field caused by a rotating gravitational lens is discussed. The influences of the Yukawa potential in quadratic gravitation on the gravitational Faraday rotation are investigated.     

从几何光学研究负折射率透镜的有限尺寸效应

从几何光学理论证明了,在左手系材料(负折率材料)透镜中存在完善聚焦的概念。当该透镜的尺寸可以认为是无穷大时,该透镜是无几何像差透镜。进一步考虑了有限透镜孔径对成像面上成像质量的影响,模拟结果表明:成像面上亮度对比度分布不均匀;且随着透镜孔径大小与厚度的比值减小,像的对比度将会增加。