Schwarzschild black hole lensing

Abstract

We study strong gravitational lensing due to a Schwarzschild black hole. Apart from the primary and the secondary images we find a sequence of images on both sides of the optic axis; we call them {\em relativistic images}. These images are formed due to large bending of light near r = 3M (the closest distance of approach r_o is greater than 3M). The sources of the entire universe are mapped in the vicinity of the black hole by these images. For the case of the Galactic supermassive ``black hole'' they are formed at about 17 microarcseconds from the optic axis. The relativistic images are not resolved among themselves, but they are resolved from the primary and secondary images. However the relativistic images are very much demagnified unless the observer, lens and source are very highly aligned. Due to this and some other difficulties the observation of these images does not seem to be feasible in near future. However, it would be a great success of the general theory of relativity in a strong gravitational field if they ever were observed and it would also give an upper bound, r_o = 3.21 M, to the compactness of the lens, which would support the black hole interpretation of the lensing object.

RevTex, 5 eps files are included, observational difficulties are discussed and there are some changes in presentation

References in corpus (2)

• Spacetime perspective of Schwarzschild lensing
• Iterative Approach to Gravitational Lensing Theory

Cited by in corpus (625)

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• Distinguishing a Slowly Accelerating Black Hole by Differential Time Delays of Images
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• Cosmological Black Holes
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• Quasinormal Modes and Topological Characteristics of a Schwarzschild Black Hole Surrounded by the Dehnen Type Dark Matter Halo
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• Light from Schwarzschild Black Holes in de Sitter expanding universe
• Constraining modified gravity theories with scalar fields using black-hole images
• On the role of strong gravity in polarization from scattering of light in relativistic flows
• Determination of the spin parameter and the inclination angle by the relativistic images in black hole image
• Iterative solutions for the gravitational lens equation in the strong deflection limit
• Black hole as an Information Eraser
• Quantum-corrected Schwarzschild AdS black hole surrounded by quintessence: Thermodynamics and Shadows
• Gravitational Lensing Effects of Fermion-Fermion Stars: I. Strong Field Case
• Study of errors in strong gravitational lensing
• Reflection from black holes and space-time topology
• Light bending and gravitational lensing in Brans-Dicke theory
• Braneworld Black Holes
• Throat effects on strong gravitational lensing in Kerr-like wormholes
• Gravitational Lensing by Black Holes in Einstein Quartic Gravity
• Black Hole Solutions and Pressure Terms in Induced Gravity with Higgs Potential
• Gravitational signatures of a nonlinear electrodynamics in $f(R,T)$ gravity
• Spectroscopy and Thermodynamics of MSW Black Hole
• On quasinormal modes in 4D black hole solutions in the model with anisotropic fluid
• Noncommutative wormhole in de Rham-Gabadadze-Tolley like massive gravity
• Radii of spherical photon orbits around Kerr-Newman black holes
• Roulettes: A weak lensing formalism for strong lensing - II. Derivation and analysis
• Through the Looking Glass into the Dark Dimension: Searching for Bulk Black Hole Dark Matter with Microlensing of X-ray Pulsars
• Analyzing Deflection Angles and Photon Sphere Dynamics of Magnetically Charged Black Holes in Nonlinear Electrodynamic
• Charged gravastar model in noncommutative geometry under $f(\mathbb{T})$ gravity
• Study of light deflection and shadow from a hairy black hole under the influence of the non-magnetic plasma
• The Erez-Rosen metric and the role of the quadrupole on light propagation
• Scalar-field Pressure in Induced Gravity with Higgs Potential and Dark Matter
• Vacuum expectation value of the energy-momentum tensor in a higher dimensional compactified cosmic string spacetime
• Observable Signatures of RN Black Holes with Dark Matter Halos via Strong Gravitational Lensing and Constraints from EHT Observations
• Kerr-Newman black hole lensing of relativistic massive particles in the weak field limit
• Strong Gravitational Lensing with Gauss-Bonnet correction
• Leading-order deflection of particles by a moving Schwarzschild lens with a two-dimensional velocity
• Black Holes as Beads on Cosmic Strings
• Black hole in a generalized Chaplygin-Jacobi dark fluid: shadow and light deflection angle
• Gravitational Lensing and Image Distortion by Buchdahl Inspired Metric in ${\mathcal{R}}^2$ Gravity
• Gravitational lensing by a stable rotating regular black hole
• Finite temperature bosonic charge and current densities in compactified cosmic string spacetime
• Interferometric signature of higher-order images in a parametrized framework
• Retrolensing by light rays slightly inside and outside of a photon sphere around a Reissner-Nordström naked singularity
• An Effective Model for the Quantum Schwarzschild Black Hole: Weak Deflection Angle, Quasinormal Modes and Bounding of Greybody Factor
• Lensing Signatures of a Slowly-Accelerated Black Hole
• Constraining deviations from spherical symmetry using $\gamma$-metric
• Massless Dirac Perturbations of black holes in f(Q) gravity: quasinormal modes and weak deflection angle
• A new asymptotical flat and spherically symmetric solution in the generalized Einstein-Cartan-Kibble-Sciama gravity and gravitational lensing
• Weak gravitational lensing by compact objects in fourth order gravity
• On the analytic generalization of particle deflection in the weak field regime and shadow size in light of EHT constraints for Schwarzschild-like black hole solutions
• Quasi-local studies of the particle surfaces and their stability in general spacetimes
• An Examination of Geometrical and Potential Time Delays in Gravitational Lensing
• Strong Lensing and Nonminimally Coupled Electromagnetism
• Optical Anisotropy of Schwarzschild Metric within Equivalent Medium Framework
• Black hole shadow and Wandering null geodesics
• The appearance of a merging binary black hole very close to a spinning supermassive black hole
• Regular scale-dependent black holes as gravitational lenses
• Gravitational Lensing of Spherically Symmetric Black Holes in Dark Matter Halos
• Gravitational lens on de-Sitter background
• Deciphering black hole phase transitions through photon spheres
• Planck-scale nonthermal correlations in a noncommutative geometry inspired Vaidya black hole
• Weak Gravitational Lensing in Ricci-Coupled Kalb-Ramond Bumblebee Gravity: Global Monopole and Axion-Plasmon Medium Effects
• Black Hole Information Problem and Wave Bursts
• A way to distinguish very compact stellar objects from black holes
• From planes to spheres: About gravitational lens magnifications
• Higher order corrections to lensing parameters for extended gravitational lenses
• Asymptotic behavior of null geodesics near future null infinity: Significance of gravitational waves
• Strong gravitational lensing of rotating regular black holes in non-minimally coupled Einstein-Yang-Mills theory
• Three Einstein rings: explicit solution and numerical simulation
• Effect of electric interaction on the deflection and gravitational lensing in the strong field limit
• Lensing and wave optics in the strong field of a black hole
• Multimodal signatures of asymptotic (A)dS Kalb-Ramond black holes: Constraints through the shadow, weak deflection angle, and topological photon spheres
• Astrophysical and electromagnetic emissivity properties of black holes surrounded by a quintessence type exotic fluid in the Scalar-Vector-Tensor Modified Gravity
• Analyzing the effect of higher dimensions on the black hole silhouette, deflection angles, and PINN approximated quasinormal modes
• Orbital motion of test particles in regular Hayward black hole space-time
• Testing black holes with cosmological constant in Einstein-bumblebee gravity through the black hole shadow using EHT data and deflection angle
• Some optical properties of rotating wormhole in Bopp-Podolsky electrodynamics
• Non-Commutative Correction to Thin Shell Collapse in Reissner Nordstr$\ddot{o}$m Geometry
• Gravitational lensing in the strong field limit for Kar's metric
• Effective gravitational mass of the Ayón-Beato and Garc\'ıa metric
• Static Vacuum Solutions on Curved Spacetimes with Torsion
• Modified Kerr black holes surrounded by dark matter spike
• Deflection and gravitational lensing with finite distance effect in the strong deflection limit in stationary and axisymmetric spacetimes
• Deflection of Light Around a Rotating BTZ Black Hole
• Energy-Momentum Distribution in General Relativity for a Phantom Black Hole Metric
• Black Holes in Lorentz-Violating Gravity: Thermodynamics, Geometry, and Particle Dynamics
• Weak gravitational lensing by an ESTGB black hole in the presence of a plasma
• Gravitational lensing in a space-time with cosmic string within the Eddington-inspired Born-Infeld gravity
• Gravitational lensing by charged black hole with global monopole in the strong field limit
• Non-Equatorial Deflection of Light due to Kerr-Newman Black Hole: A Material Medium Approach
• Relativistic effects cannot explain galactic dynamics
• Circular light orbits of a general, static, and spherical symmetrical wormhole with $Z_2$ symmetry
• Correspondence between two gravitational lens equations in a static and spherically symmetric spacetime
• A spinorial proof of the rigidity of the Riemannian Schwarzschild manifold
• Static spheres and Aschenbach effect for black holes in massive gravity
• Gravitational lensing signature of matter distribution around Schwarzschild black hole
• Lensing and imaging by a stealth defect of spacetime
• Static Spherical Vacuum Solution to Bumblebee Gravity with Time-like VEVs
• Microlensing and event rate of static spherically symmetric wormhole
• Gravitational lensing of wormholes in noncommutative geometry
• Testing black holes in a perfect fluid dark matter environment using quasinormal modes
• Strong gravitational lensing effects around rotating regular black holes
• Gravitational lensing in holonomy corrected spherically symmetric black holes with phantom global monopoles
• A generalization of photon sphere based on escape/capture cone
• Imprints of a gravitational wave through the weak field deflection of photons
• Singularity in Gravitational Collapse of Plane Symmetric Charged Vaidya Spacetime
• Timelike orbits around accelerating black holes
• Asymptotic behavior of null geodesics near future null infinity II: curvatures, photon surface and dynamically transversely trapping surface
• Galactic microlensing by backreacted massless wormholes
• Analyzing the Influence of Geometrical Deformation on Photon Sphere and Shadow Radius: A New Analytical Approach -Stationary, and Axisymmetric Spacetime
• Analytical time-like geodesics in modified Hayward black hole space-time
• Traces of quantum fuzziness on the black hole shadow and particle deflection in the multi-fractional theory of gravity
• Strong gravitational lensing by black hole in F(R) Euler Heisenberg Gravity's Rainbow
• Relevant scales for the $C$-metric with positive cosmological constant
• Gravitational lensing of STU black holes
• Cylindrical black hole solutions in $f(\mathcal{R})$ and $f(\mathcal{R},\mathcal{A},A^{\mu \nu }{A}_{\mu \nu })$ modified gravity
• Bending of Light and Inhomogeneous Picard-Fuchs Equation
• Probing the gravitational Faraday rotation using quasar X-ray microlensing
• Lensing Stability and Scattering Phenomena in Anisotropic Black Hole Spacetimes in Plasma
• Null Gravitational Redshift by a Reissner-Nordström Black Hole in the Strong Field Limit
• Overlapping of photon rings in black hole imaging
• Strong Lensing Effect and Quasinormal Modes of Oscillations of Black Holes in $\mathbf{f}(\mathbf{R},\mathbf{T})$ Gravity Theory
• Shadow of Kerr black hole surrounded by a cloud of strings in Rastall gravity and constraints from M87*
• Gravitational Lensing by a Dark Compact Object in Modified Gravity and Observational Constraints from Einstein Rings
• Shadows of a generic class of spherically symmetric, static spacetimes
• Localization of Energy and Momentum in an Asymptotically Reissner-Nordström Non-singular Black Hole Space-time Geometry
• Quantum Gravitational Hair in Gravastars and Observational Tests
• Strong Gravitational Lensing Effects of the Rotating Short-Haired Black Hole and Constraints from EHT Observations
• Aberration effect on lower-order images of thin accretion disk in the astrometric approach
• Strong gravitational lensing around Kehagias-Sfetsos compact objects surrounded by plasma
• Uniqueness of photon sphere for Reissner-Nordström electric-magnetic system
• Observable strong field effects of extra spacetime dimension in the braneworld black hole
• Gauss-Bonnet lensing of spinning massive particles in static spherically symmetric spacetimes
• A full waveform model for arbitrarily axis-symmetric black hole mergers
• On the global Gaussian bending measure and its applications in stationary spacetimes
• A General Discussion on Photon Spheres in Different Categories of Spacetimes
• Gravitational Lensing of Euler-Heisenberg Black Hole Surrounded by Perfect Fluid Dark Matter
• Exploring the role of accretion disk geometry in shaping black hole shadows
• Probing dark fluids and modified gravity with gravitational lensing
• Gravitational Black Hole Shadow Spectroscopy
• Boundary-only weak deflection angles from isothermal optical geometry
• Finite temperature charge and current densities around a cosmic string in AdS spacetime with compact dimension
• Lensing by black holes within astrophysical environments
• Strong gravitational lensing by a Reissner-Nordström naked singularity with a marginally unstable photon sphere
• Shedding Light on Gravity: Black Hole Shadows and Lensing Signatures in Lorentz Gauge Theory
• Cusp Summations and Cusp Relations of Simple Quad Lenses
• Gravitational deflection of light in polar-axis plane of a moving Kerr-Newman black hole
• Photon spheres near black holes in a model with anisotropic fluid
• Gravitational lensing inside and outside of a marginally unstable photon sphere in a general, static, spherically symmetric, and asymptotically-flat spacetime in strong deflection limits
• Strong-deflection expansion of the deflection angle near a degenerate photon sphere
• From GLC to double-null coordinates and illustration with static black holes
• Lensing, Shadow and Photon Rings in a Magnetized Black Hole Spacetime
• Einstein ring of dust shells with quantum hair
• Particle Deflections around Microscopic Loop Quantum Black Holes with Rigorous Quantum Parameters
• Axisymmetric black hole in a non-commutative gauge theory: classical and quantum gravity effects
• Strong Gravitational Lensing by Compact Object without Cauchy Horizons in Effective Quantum Gravity
• The precession of particle spin in spherical symmetric spacetimes
• Null geodesics around a black hole with weakly coupled global monopole charge
• Examining the Kerr Metric through Wave Fronts of Null Geodesics
• Gravitational lensing by two photon spheres in a black-bounce spacetime in strong deflection limits
• Strong gravitational lensing of a five-dimensional charged, equally rotating black hole with a cosmological constant
• Light propagation around a Kerr-like black hole immersed in an inhomogeneous anisotropic plasma in Rastall gravity: Analytical solutions to the equations of motion
• Gravitational lensing, memory and the Penrose limit
• Charged traversable wormholes: charge without charge
• Deflection of light and time delay in hyperbolic Einstein-Straus--de Sitter solution
• Static Manifolds with Boundary and Rigidity of Scalar Curvature and Mean Curvature
• Deflection of light due to spheroidal oblate static objects
• Periodic Gravitational Lensing with Oscillating Boson Stars
• Black Hole and Equipotential Photon Surface Uniqueness in 4-dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes
• Image of a quantum-corrected black hole without Cauchy horizons illuminated by a static thin accretion disk
• Fixed energy solutions to the Euler-Lagrange equations of an indefinite Lagrangian with affine Noether charge
• Galactic microlensing by acoustic Schwarzschild black holes
• Strong gravitational lensing effects of black holes with quantum hair
• Vacuum polarization effects in the background of a deformed compact object and implications for photon velocity
• Distinguish Bardeen-like black holes by Gravitational lensing
• Light propagation and quasinormal modes of a topologically charged Schwarzschild-Klinkhamer wormhole
• Gravitational aspects of a new bumblebee black hole
• Deflection of Light and Shapiro Delay: An Equivalent Medium Theory Approach
• Revisiting Einstein's analogy: black holes as gradient-index lenses
• Optical and orbital characterization of spherically symmetric static black holes of self-gravitating new nonlinear electrodynamics model
• General Non-Static Spherically Symmetric Solutions of Einstein Vaccum Field Equations with Lambda
• Electroweak Corrections to Photon Scattering, Polarization and Lensing in a Gravitational Background and the Near Horizon Limit
• How to distinguish an actual astrophysical magnetized black hole mimicker from a true (theoretical) black hole
• Revisiting The Gravitational Mirroring In Presence of Compact Objects
• Probing Quantum Gravity in Stellar Spacetimes: Phenomenological Insights
• Higher-dimensional electric-magnetic photon sphere uniqueness
• Two Black Hole Holography, Lensing and Intensity
• Gravitational lensing by a black hole in Poincar{é} gauge theory of gravity
• Finite temperature energy-momentum tensor in compactified cosmic string spacetime
• Photon surfaces, shadows and accretion disks in gravity with minimally coupled scalar field
• Continuous image distortion by astrophysical thick lenses
• Strong lensing and Observables around 5D Myers-Perry black hole spacetime
• Gravitational Deflection of Vector Photons via Effective Field Theory
• Optical appearance of regularized compact objects without an exterior photon sphere
• What are the parities of photon-ring images near a black hole?
• Behavior of vacuum and naked singularity under smooth gauge function in Lyra geometry
• Strong gravitational lensing for the charged black holes with scalar hair
• Analytical approach for calculating shadow of dynamical black hole
• Decoding a black hole metric from the interferometric pattern of the relativistic images of a compact source
• Geodesics and Bending of Light around a BTZ Black Hole Surrounded by Quintessential Matter
• Investigating the effects of gravitational lensing by Hu-Sawicki $\mathbf{f}(\mathbf{R})$ gravity black holes
• Strong field gravitational lensing of particles by a black-bounce-Schwarzschild black hole
• Relativistic Einstein Rings of Reissner-Nordström metric Black Holes Nonminimally Coupled to Electrodynamics
• Spacetime Perspective of Gravitational Lensing in Perturbed Cosmologies
• Topological charge and black hole photon spheres in massive gravity
• Uniqueness of electric-magnetic spacetimes with massive particle
• Real-time High-Quality Rendering of Non-Rotating Black Holes
• Light deflection in axially symmetric stationary spacetimes filled with a moving medium
• Existence of steady states of the massless Einstein-Vlasov system surrounding a Schwarzschild black hole
• Gravitational Lensing Effect from The Revised Deser-Woodard Nonlocal Gravity
• On the energy of a non-singular black hole solution satisfying the weak energy condition
• Conformal-symmetry wormholes supported by a perfect fluid
• Effect of primary scalar hair on black hole's strong lensing in Beyond Horndeski Gravity
• Charged galactic wormholes: shadow imaging, accretion disks, and charged-particle deflection
• Shadows and photon spheres of static black holes embedded in a Dehnen-(1,4,5/2)-type dark matter halo with a quintessential field
• The Yilmaz-Rosen and Janis-Newman-Winicour metric solutions in the scalar-Einstein-Gauss-Bonnet $4d$ gravitational model
• Angular Location of the $n^{th}$ Einstein Ring at large $n$
• Measuring black hole spin through gravitational lensing of pulsars
• Strong deflection of massive particles via the geodesic deviation equation
• Phenomenology of Schwarzschild-like Black Holes with a Generalized Compton Wavelength
• Gravitational lensing observables in stationary and axisymmetric solutions in general relativity