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A review on analytical studies in Gravitational Lensing
General Relativity and Quantum Cosmology · Submitted 3 Mar 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Furthermore, we extend our studies for a particular class of newly proposed solutions called black-bounce spacetimes and discuss throughout the review how to explore lensing in these spacetimes and how the various parameters can be constrained using available astrophysical and cosmological data.
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The abstract, sentence by sentence
In this study, we review some current studies on Gravitational Lensing for black holes, mainly in the context of general relativity. We mainly focus on the analytical studies related to lensing with references to observational results. We start with reviewing lensing in spherically symmetric Schwarzschild spacetime, showing how to calculate deflection angles before moving to the rotating counterpart, the Kerr metric. Furthermore, we extend our studies for a particular class of newly proposed solutions called black-bounce spacetimes and discuss throughout the review how to explore lensing in these spacetimes and how the various parameters can be constrained using available astrophysical and cosmological data.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this study, we review some current studies on Gravitational Lensing for black holes, mainly in the context of general relativity. | contribution 0.93 | 0.60 | 0.05 | asserted 0.73 |
| s1 | We mainly focus on the analytical studies related to lensing with references to observational results. | contribution 0.80 | 0.52 | 0.05 | asserted 0.91 |
| s2 | We start with reviewing lensing in spherically symmetric Schwarzschild spacetime, showing how to calculate deflection angles before moving to the rotating counterpart, the Kerr metric. | method 0.66 | 0.45 | 0.04 | asserted 0.99 |
| s3 | Furthermore, we extend our studies for a particular class of newly proposed solutions called black-bounce spacetimes and discuss throughout the review how to explore lensing in these spacetimes and how the various parameters can be constrained using available astrophysical and cosmological data. | contribution 0.98 | 0.48 | 0.15 | asserted 0.89 |
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The paper
Original abstract
In this study, we review some current studies on Gravitational Lensing for black holes, mainly in the context of general relativity. We mainly focus on the analytical studies related to lensing with references to observational results. We start with reviewing lensing in spherically symmetric Schwarzschild spacetime, showing how to calculate deflection angles before moving to the rotating counterpart, the Kerr metric. Furthermore, we extend our studies for a particular class of newly proposed solutions called black-bounce spacetimes and discuss throughout the review how to explore lensing in these spacetimes and how the various parameters can be constrained using available astrophysical and cosmological data.
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References
How the literature uses it
23 arXiv papers cite this in 24 sentences
Papers citing it · 8 sentences without a confident label
Cites it as background 15 papers
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In recent years, the weak- and strong-field gravitational lens effects of light signals in the black-bounce-Schwarzschild spacetime or in the generalized versions [ref] of this geometry have been of growing interest [ref] .
Gravitational lensing of massive particles by a black-bounce-Schwarzschild black hole · Introduction · 0.84
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At first glance, the correspondence is quite surprising, as vibrational properties of the event horizon, the quasinormal modes (QNMs) [ref] , are associated with its optical appearance [ref] .
Trinity of black hole correspondences: Shadows, quasinormal modes, graybody factors, and cautionary remarks · Introduction · 0.98
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To actually probe the spacetime geometry nearest the event horizon, light can traverse a BH in the orbits called photon-rings which constitute the photon sphere [ref] , whereas the dark region inside the photon sphere is termed as the black hole shadow, see [ref] for a review.
Effect of magnetized plasma on shadow and gravitational lensing of a Reissner-Nordstr\"om black hole · Introduction · 0.97
What it cites · 107 sentences without a confident label
Builds on 4 papers
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A lens equation has been derived in [ref] , which has been further generalized in [ref] where the underlying black hole serves as a lens.
A comparison of approximate gravitational lens equations and a proposal for an improved new one · Introduction · 0.81
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A lens equation has been derived in [ref] , which has been further generalized in [ref] where the underlying black hole serves as a lens.
Schwarzschild black hole lensing · Introduction · 0.81
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Later it was extended for rotating black holes in [ref] .
Quasi-Equatorial Gravitational Lensing by Spinning Black Holes in the Strong Field Limit · Introduction · 0.92
Uses the method or tool of 6 papers
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The computation details are given in [ref] .
Analytical study of gravitational lensing in Kerr-Newman black-bounce spacetime · Perturbative computation of the deflection angle: analytical results · 0.85
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We can follow the same method as mentioned in Sec. ([ref]) to extract the divergent part as well as the finite part of the deflection angle as the function $ω(r).$ They are given by, [equation] where, [equation] and [equation] Our interest is to find the position of the caustics, where the magnification diverges, and is given in [ref] , $γ̅_̅k̅=-b̅+a̅(b̂-k π)$.
Quasi-Equatorial Gravitational Lensing by Spinning Black Holes in the Strong Field Limit · Non-equatorial Lensing · 0.98
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To find out the roots, we need to substitute equations ([ref]) to ([ref]) into ([ref]) and compare it with the coefficients of $u^0,u^2,u^3,u^4$ in ([ref]) we will get [ref] , [equation] Exactly mimicking the same procedure as Sec ([ref]) one can write down the expression of deflection angle upto $𝒪(l^2)$ and the correction term is given by, [equation] where, [equation] and, $χ_1$ and $χ_2$ is given by, [equation] and [equation] $Π(ψ_0,α^2,k)$ and $Π(π/2,α^2,k)$ are the incomplete and complete elliptic integrals of the third kind, respectively.
Equatorial light bending around Kerr-Newman black holes · Perturbative computation of the deflection angle: analytical results · 0.87
Uses data or values from 1 paper
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Some of the values provided in ([ref] and [ref]) are reproduced from [ref] .
Analytical study of gravitational lensing in Kerr-Newman black-bounce spacetime · Observational signature in strong deflection limit · 1.00
Compares with 3 papers
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Furthermore, we can reproduce the result for the Reissner-Nordstrom black hole in the limit, $a=0$, and the root of the equation ([ref]) then reduce to, [equation] where $r_c$ is defined in ([ref]) and the result ([ref]) matches with the result of [ref] .
Equatorial light bending around Kerr-Newman black holes · Details of the computation of the deflection angle for Kerr-Newman Spacetime · 0.93
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Comparing the values in Table ([ref]) and ([ref]) we can conclude that the change of caustic points for different $Q$ and different $l$ is not that robust [ref] .
Analytical study of gravitational lensing in Kerr-Newman black-bounce spacetime · Results for non equatorial lensing: caustic points · 0.84
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From ([ref]), one can easily check that, when $Q$ becomes zero, $δ$ becomes $π.$ In that limit, ([ref]) can be written as, [equation] It then exactly reproduces the result for the Kerr black hole [ref] .
Light's Bending Angle in the Equatorial Plane of a Kerr Black Hole · Details of the computation of the deflection angle for Kerr-Newman Spacetime · 0.96
Cites as background 13 papers
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Furthermore, in recent times, several static metrics known as Black Bounce metric have been proposed in [ref] .
Black-bounce to traversable wormhole · Introduction · 0.84
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Furthermore, in recent times, several static metrics known as Black Bounce metric have been proposed in [ref] .
Charged black-bounce spacetimes · Introduction · 0.84
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Furthermore, in recent times, several static metrics known as Black Bounce metric have been proposed in [ref] .
A novel family of rotating black hole mimickers · Introduction · 0.84
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