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Universe
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Gravitational Lensing and Optical Geometry: A Centennial Perspective
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Gravitational Lensing and Optical Geometry: A Centennial Perspective

A special issue of Universe (ISSN 2218-1997).

Deadline for manuscript submissions: closed (31 March 2020) | Viewed by 21837

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Prof. Dr. Marcus C. Werner

E-Mail Website
Guest Editor
Zu Chongzhi Center for Mathematics and Computational Sciences, Duke Kunshan University, Kunshan 215316, China
Interests: modified gravity theories; construction and tests; gravitational lensing; gravitational waves

Special Issue Information

Dear Colleagues,

The year 2019 sees the centenary of Eddington's eclipse expeditions and the corroboration of Einstein's general relativity by gravitational lensing. To mark the occasion, you are cordially invited to contribute to this Special Issue dedicated to theoretical aspects of strong gravitational lensing. A variety of mathematical approaches have been applied to study this effect, both in 3-space and in spacetime. In particular, we will consider the following:

  • Mathematical properties of the standard thin lens approximation, for instance image multiplicity and topology; complex formalism and lensing invariants;
  • Optical geometry, both Riemannian for static spacetimes, and Randers–Finsler for stationary spacetimes; the Gauss–Bonnet method and related approaches;
  • Lensing in the spacetime of general relativity and of modified and higher-dimensional theories, for instance properties of photon spheres and rings; black hole shadows;

Contributions discussing such lensing properties for gravitational waves will be appreciated as well. Moreover, historical surveys related to this topic are also welcome.

Thank you in advance for your consideration.

With best regards,

Dr. Marcus Werner
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Universe is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Gravitational lensing
  • Optical geometry
  • General relativity
  • Modified gravity theories

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Published Papers (6 papers)

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Research

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23 pages, 2452 KiB  
Article
Caustics in Gravitational Lensing by Mixed Binary Systems
by Valerio Bozza, Silvia Pietroni and Chiara Melchiorre
Universe 2020, 6(8), 106; https://doi.org/10.3390/universe6080106 - 31 Jul 2020
Cited by 9 | Viewed by 3282
Abstract
We investigated binary lenses with 1/rn potentials in the asymmetric case with two lenses with different indexes n and m. These kinds of potentials have been widely used in several contexts, ranging from galaxies with halos described by different [...] Read more.
We investigated binary lenses with 1/rn potentials in the asymmetric case with two lenses with different indexes n and m. These kinds of potentials have been widely used in several contexts, ranging from galaxies with halos described by different power laws to lensing by wormholes or exotic matter. In this paper, we present a complete atlas of critical curves and caustics for mixed binaries, starting from the equal-strength case, and then exploring unequal-strength systems. We also calculate the transitions between all different topology regimes. Finally we find some useful analytic approximations for the wide binary case and for the extreme unequal-strength case. Full article
(This article belongs to the Special Issue Gravitational Lensing and Optical Geometry: A Centennial Perspective)
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18 pages, 2305 KiB  
Article
Shadow Images of a Rotating Dyonic Black Hole with a Global Monopole Surrounded by Perfect Fluid
by Sumarna Haroon, Kimet Jusufi and Mubasher Jamil
Universe 2020, 6(2), 23; https://doi.org/10.3390/universe6020023 - 24 Jan 2020
Cited by 45 | Viewed by 3413
Abstract
In this paper, we revisit the rotating global monopole metric and extend the metric to a rotating dyonic global monopole in the presence of a perfect fluid. We then show that the surface topology at the event horizon, related to the metric computed, [...] Read more.
In this paper, we revisit the rotating global monopole metric and extend the metric to a rotating dyonic global monopole in the presence of a perfect fluid. We then show that the surface topology at the event horizon, related to the metric computed, is a 2-sphere using the Gauss-Bonnet theorem. By choosing ω = − 1 / 3 , 0 , 1 / 3 we investigate the effect of dark matter, dust and radiation on the silhouette of a black hole. The presence of the global monopole parameter γ and the perfect fluid parameters υ also deform the shape of a black hole’s shadow, which has been depicted through graphical illustrations. Finally, we analyse the energy emission rate of a rotating dyonic global monopole surrounded by perfect fluid with respect to parameters. Full article
(This article belongs to the Special Issue Gravitational Lensing and Optical Geometry: A Centennial Perspective)
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13 pages, 391 KiB  
Article
EHT Constraint on the Ultralight Scalar Hair of the M87 Supermassive Black Hole
by Pedro V. P. Cunha, Carlos A. R. Herdeiro and Eugen Radu
Universe 2019, 5(12), 220; https://doi.org/10.3390/universe5120220 - 27 Nov 2019
Cited by 113 | Viewed by 3802
Abstract
Hypothetical ultralight bosonic fields will spontaneously form macroscopic bosonic halos around Kerr black holes, via superradiance, transferring part of the mass and angular momentum of the black hole into the halo. Such a process, however, is only efficient if resonant—when the Compton wavelength [...] Read more.
Hypothetical ultralight bosonic fields will spontaneously form macroscopic bosonic halos around Kerr black holes, via superradiance, transferring part of the mass and angular momentum of the black hole into the halo. Such a process, however, is only efficient if resonant—when the Compton wavelength of the field approximately matches the gravitational scale of the black hole. For a complex-valued field, the process can form a stationary, bosonic field black hole equilibrium state—a black hole with synchronised hair. For sufficiently massive black holes, such as the one at the centre of the M87 supergiant elliptic galaxy, the hairy black hole can be robust against its own superradiant instabilities, within a Hubble time. Studying the shadows of such scalar hairy black holes, we constrain the amount of hair which is compatible with the Event Horizon Telescope (EHT) observations of the M87 supermassive black hole, assuming the hair is a condensate of ultralight scalar particles of mass μ ∼ 10 − 20 eV, as to be dynamically viable. We show the EHT observations set a weak constraint, in the sense that typical hairy black holes that could develop their hair dynamically, are compatible with the observations, when taking into account the EHT error bars and the black hole mass/distance uncertainty. Full article
(This article belongs to the Special Issue Gravitational Lensing and Optical Geometry: A Centennial Perspective)
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7 pages, 1529 KiB  
Article
Magnification Cross Sections for the Elliptic Umbilic Caustic Surface
by Amir B. Aazami, Charles R. Keeton and Arlie O. Petters
Universe 2019, 5(7), 161; https://doi.org/10.3390/universe5070161 - 2 Jul 2019
Cited by 2 | Viewed by 2822
Abstract
In gravitational lensing, magnification cross sections characterize the probability that a light source will have magnification greater than some fixed value, which is useful in a variety of applications. The (area) cross section is known to scale as μ − 2 for fold [...] Read more.
In gravitational lensing, magnification cross sections characterize the probability that a light source will have magnification greater than some fixed value, which is useful in a variety of applications. The (area) cross section is known to scale as μ − 2 for fold caustics and μ − 2.5 for cusp caustics. We aim to extend the results to higher-order caustic singularities, focusing on the elliptic umbilic, which can be manifested in lensing systems with two or three galaxies. The elliptic umbilic has a caustic surface, and we show that the volume cross section scales as μ − 2.5 in the two-image region and μ − 2 in the four-image region, where μ is the total unsigned magnification. In both cases our results are supported both numerically and analytically. Full article
(This article belongs to the Special Issue Gravitational Lensing and Optical Geometry: A Centennial Perspective)
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10 pages, 264 KiB  
Article
Deflection Angle of Photons through Dark Matter by Black Holes and Wormholes Using Gauss–Bonnet Theorem
by Ali Övgün
Universe 2019, 5(5), 115; https://doi.org/10.3390/universe5050115 - 14 May 2019
Cited by 75 | Viewed by 3527
Abstract
In this research, we used the Gibbons–Werner method (Gauss–Bonnet theorem) on the optical geometry of a black hole and wormhole, extending the calculation of weak gravitational lensing within the Maxwell’s fish eye-like profile and dark-matter medium. The angle is seen as a partially [...] Read more.
In this research, we used the Gibbons–Werner method (Gauss–Bonnet theorem) on the optical geometry of a black hole and wormhole, extending the calculation of weak gravitational lensing within the Maxwell’s fish eye-like profile and dark-matter medium. The angle is seen as a partially topological effect, and the Gibbons–Werner method can be used on any asymptotically flat Riemannian optical geometry of compact objects in a dark-matter medium. Full article
(This article belongs to the Special Issue Gravitational Lensing and Optical Geometry: A Centennial Perspective)

Review

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44 pages, 1301 KiB  
Review
The Effects of Finite Distance on the Gravitational Deflection Angle of Light
by Toshiaki Ono and Hideki Asada
Universe 2019, 5(11), 218; https://doi.org/10.3390/universe5110218 - 1 Nov 2019
Cited by 46 | Viewed by 3685
Abstract
In order to clarify the effects of the finite distance from a lens object to a light source and a receiver, the gravitational deflection of light has been recently reexamined by using the Gauss–Bonnet (GB) theorem in differential geometry (Ishihara et al. 2016). [...] Read more.
In order to clarify the effects of the finite distance from a lens object to a light source and a receiver, the gravitational deflection of light has been recently reexamined by using the Gauss–Bonnet (GB) theorem in differential geometry (Ishihara et al. 2016). The purpose of the present paper is to give a short review of a series of works initiated by the above paper. First, we provide the definition of the gravitational deflection angle of light for the finite-distance source and receiver in a static, spherically symmetric and asymptotically flat spacetime. We discuss the geometrical invariance of the definition by using the GB theorem. The present definition is used to discuss finite-distance effects on the light deflection in Schwarzschild spacetime for both the cases of weak deflection and strong deflection. Next, we extend the definition to stationary and axisymmetric spacetimes. We compute finite-distance effects on the deflection angle of light for Kerr black holes and rotating Teo wormholes. Our results are consistent with the previous works if we take the infinite-distance limit. We briefly mention also the finite-distance effects on the light deflection by Sagittarius A*. Full article
(This article belongs to the Special Issue Gravitational Lensing and Optical Geometry: A Centennial Perspective)
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