Chaotic Shadows of Black Holes: A Short Review

Abstract

We give a brief review on the formation and the calculation of black hole shadow. Firstly, we introduce the conception of black hole shadow and the current works on a variety of black hole shadows. Secondly, we present main methods of calculating photon sphere radius and shadow radius, and then explain how the photon sphere affect the boundary of black hole shadow. We review the analytical calculation for black hole shadows which have analytic expressions for shadow boundary due to the integrable photon motion system. And we introduce the fundamental photon orbits which can explain the patterns of black hole shadow shape. Finally, we review the numerical calculation of black hole shadows with the backward ray-tracing method, and introduce some chaotic black hole shadows with self-similar fractal structures. Since the gravitational waves from the merger of binary black holes have been detected, we introduce a couple of shadows of binary black holes, which all have the eyebrowlike shadows around the main shadows with the fractal structures. We discuss the invariant phase space structures of photon motion system in black hole space-time, and explain the formation of black hole shadow is dominated by the invariant manifolds of certain Lyapunov orbits near the fixed points.

arXiv comment16 Pages, 18 figures, An invited short review and accepted for publication in Commun. Theor. Phys. Some minor error in the original version are corrected

References in corpus (85)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2
• GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
• First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring
• GW170608: Observation of a 19-solar-mass Binary Black Hole Coalescence
• Viewing the Shadow of the Black Hole at the Galactic Center
• First M87 Event Horizon Telescope Results. II. Array and Instrumentation
• First M87 Event Horizon Telescope Results. III. Data Processing and Calibration
• Shadows and strong gravitational lensing: a brief review
• Shadows of Kerr black holes with scalar hair
• GW150914: First results from the search for binary black hole coalescence with Advanced LIGO
• Measurement of the Kerr Spin Parameter by Observation of a Compact Object's Shadow
• Photon Regions and Shadows of Kerr-Newman-NUT Black Holes with a Cosmological Constant
• Influence of a plasma on the shadow of a spherically symmetric black hole
• Shadow of rotating regular black holes
• Shadow of a black hole surrounded by dark matter
• A new method for shadow calculations: application to parameterised axisymmetric black holes
• Apparent shape of super-spinning black holes
• Shadow of a rotating braneworld black hole
• Observing the shadow of Einstein-Maxwell-Dilaton-Axion black hole
• Shapes and Positions of Black Hole Shadows in Accretion Disks and Spin Parameters of Black Holes
• Null geodesics and shadow of a rotating black hole in extended Chern-Simons modified gravity
• Black hole shadow in an asymptotically-flat, stationary, and axisymmetric spacetime: The Kerr-Newman and rotating regular black holes
• Shadow of a Kaluza-Klein rotating dilaton black hole
• Optical properties of black hole in the presence of plasma: shadow
• Photon Rings around Kerr and Kerr-like Black Holes
• A coordinate-independent characterization of a black hole shadow
• The Shadow of a Rotating Traversable Wormhole
• Black Hole Parameter Estimation from Its Shadow
• Shadows and photon spheres with spherical accretions in the four-dimensional Gauss-Bonnet black hole
• Black hole shadow in an expanding universe with a cosmological constant
• Chaotic lensing around boson stars and Kerr black holes with scalar hair
• Light propagation in a plasma on Kerr spacetime: Separation of the Hamilton-Jacobi equation and calculation of the shadow
• Black Hole Surrounded by a Dark Matter Halo in the M87 Galactic Center and its Identification with Shadow Images
• Influence of quintessence dark energy on the shadow of black hole
• Shadows of Kerr black holes with and without scalar hair
• Fundamental photon orbits: black hole shadows and spacetime instabilities
• Shadows of rotating wormholes
• Measuring the Kerr spin parameter of regular black holes from their shadow
• Shadow of a Spinning Black Hole in an Expanding Universe
• Gravitational Lensing in presence of Plasma: Strong Lens Systems, Black Hole Lensing and Shadow
• Shadows of Multi-Black Holes: Analytic Exploration
• Curvature radius and Kerr black hole shadow
• Black Hole Shadow of Sgr A${}^{\ast }$ in Dark Matter Halo
• Shadow casted by a Konoplya-Zhidenko rotating non-Kerr black hole
• Shadow analysis for rotating black holes in the presence of plasma for an expanding universe
• On the shadow of rotating traversable wormholes
• Lensing and shadow of a black hole surrounded by a heavy accretion disk
• Energetics and optical properties of $6$-dimensional rotating black hole in pure Gauss-Bonnet gravity
• What does a binary black hole merger look like?
• Binary black hole shadows, chaotic scattering and the Cantor set
• Shadow cast by rotating braneworld black holes with a cosmological constant
• Astrophysical imaging of Kerr black holes with scalar hair
• Axion-plasmon or magnetized plasma effect on an observable shadow and gravitational lensing of a Schwarzschild black hole
• Shadows and lensing of black holes immersed in strong magnetic fields
• Shadows of Bonnor black dihole by chaotic lensing
• Black Hole Images as Tests of General Relativity: Effects of Spacetime Geometry
• Chaotic shadow of a non-Kerr rotating compact object with quadrupole mass moment
• Intrinsic curvature and topology of shadows in Kerr spacetime
• Revisiting the shadow of a black hole in the presence of a plasma
• Shadows of CPR black holes and tests of the Kerr metric
• Shadow of a Charged Rotating Black Hole in $f(R)$ Gravity
• Shadow of nulllike and timelike naked singularities without photon spheres
• Evolution of black hole shadow in the presence of ultralight bosons
• Comparing Gravitational Waveform Extrapolation to Cauchy-Characteristic Extraction in Binary Black Hole Simulations
• A Parametric model for the shapes of black-hole shadows in non-Kerr spacetimes
• Shadow of a rotating squashed Kaluza-Klein black hole
• Asymptotically flat, parameterized black hole metric preserving Kerr symmetries
• Polarization effects in Kerr black hole shadow due to the coupling between photon and bumblebee field
• Double shadow of a regular phantom black hole as photons couple to Weyl tensor
• Shadows of Exact Binary Black Holes
• Kerr Black hole shadows in Melvin magnetic field with stable photon orbits
• Shadow of a naked singularity
• Black hole shadow to probe modified gravity
• Shadows of Colliding Black Holes
• Black Hole Shadows and Invariant Phase Space Structures
• Possible imprints of cosmic strings in the shadows of galactic black holes
• Shadow of a Schwarzschild black hole surrounded by a Bach-Weyl ring
• Gravitational effect of plasma particles on the shadow of Schwarzschild black holes
• Effect of gravitational wave on shadow of a Schwarzschild black hole
• Qualifying ringdown and shadow of black holes under general parametrized metrics with photon orbits
• Testing the Kerr Paradigm with the Black Hole Shadow

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• Light rings and shadows of static black holes in effective quantum gravity
• Kerr black holes with synchronised Proca hair: lensing, shadows and EHT constraints
• Shape of higher-order images of equatorial emission rings around a Schwarzschild black hole: Analytical description with polar curves
• Quasinormal modes-shadow correspondence for rotating regular black holes
• Deflection angle and shadow of the Reissner-Nordström black hole with higher-order magnetic correction in Einstein-nonlinear-Maxwell fields
• Shadow of slowly rotating Kalb-Ramond black holes
• Gravitational Lensing of Schwarzschild and Charged Black Holes Immersed in Perfect Fluid Dark Matter Halo
• Curvatures, Photon Spheres and Black Hole Shadows
• Trinity of black hole correspondences: Shadows, quasinormal modes, graybody factors, and cautionary remarks
• Shadows of rotating Einstein-Maxwell-dilaton black holes surrounded by a plasma
• Light rings and shadows of static black holes in effective quantum gravity II: A new solution without Cauchy horizons
• Using the shadow of a black hole to examine the energy exchange between axion matter and a rotating black hole
• Determination of the spin parameter and the inclination angle by the relativistic images in black hole image
• The ring-shaped shadow of rotating naked singularity with a complete photon sphere
• The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis
• Motion of particles around a magnetically charged Euler-Heisenberg black hole with scalar hair and the Event Horizon Telescope
• Fractal signatures of non-Kerr spacetimes in the shadow of light-ring bifurcations
• The surface geometry and shadow of a Schwarzschild black hole with halo
• Shadows cast by a class of rotating black bounces with an anisotropic fluid
• Photon region boundary for stationary axisymmetric black holes
• Motion equations in a Kerr-Newman-de Sitter spacetime: some methods of integration and application to black holes shadowing in Scilab