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Calculating black hole shadows: Review of analytical studies
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In this article, we provide a review of the current state of the research of the black hole shadow, focusing on analytical (as opposed to numerical and observational) studies. We start with particular attention to the definition of the shadow and its relation to the often used concepts of escape cone, critical impact parameter and particle cross-section. For methodological purposes, we present the derivation of the angular size of the shadow for an arbitrary spherically symmetric and static space-time, which allows one to calculate the shadow for an observer at arbitrary distance from the center. Then we discuss the calculation of the shadow of a Kerr black hole, for an observer anywhere outside of the black hole. For observers at large distances we present and compare two methods used in the literature. Special attention is given to calculating the shadow in space-times which are not asymptotically flat. Shadows of wormholes and other black-hole impostors are reviewed. Then we discuss the calculation of the black hole shadow in an expanding universe as seen by a comoving observer. The influence of a plasma on the shadow of a black hole is also considered.
Forward citations
Cited by 28 Pith papers
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Regular Vaidya solutions of effective gravitational theories
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On Black Holes Surrounded by Radiation: I. Classical Considerations
Presents classical GR solutions for black holes enveloped by ultra-relativistic orbiting particle shells that extend the photon sphere to arbitrary depth while remaining optically indistinguishable from standard black holes.
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Higher-Derivative Corrections to Reissner--Nordstr\"om Black Holes from Worldline QFT
RF² corrections to RN black holes are computed via worldline QFT, verified exactly in G, and shown to require the weak gravity conjecture for non-negative extremal temperature.
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Shadow dependent phenomenology framework for rotating black hole metric
A thermodynamic-optical duality reparameterizes black hole mass via observable shadow radius to derive lensing angles, Hawking temperature, and luminosity for Kerr, Kerr-MOG, and rotating Horndeski metrics, yielding m...
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Reshaping the inner shadow of a Kerr black hole by a torn accretion disk
Torn accretion disks around Kerr black holes erode the inner shadow and create bifurcated, crescent, and multi-ring shadow features driven by sub-disk discontinuities and outer tilt angle.
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Gravity/thermodynamics correspondence via black hole shadows
Cuspy black hole shadows correspond to swallowtail thermodynamic free energy, with boundary self-intersections marking geometric phase transitions whose critical exponents fall in the mean-field class.
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On the Cuspy Structure of Rotating Wormhole Shadows
Rotating wormhole shadows develop cusps above a universal critical redshift value λ_c, yielding four morphologies: smooth, cuspy, ears touching, and throat drowning.
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Shadow, acoustic redshift, and transfer observables of Lorentz-violating rotating acoustic black holes
Derives shadow width, redshift asymmetry, and flux observables for the Lorentz-violating draining-bathtub acoustic black hole, showing how each observable isolates different combinations of the rotation and violation ...
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Constraints on Schwarzschild Black Hole in a Generalized Dehnen-Type $(1,4,\gamma)$ Dark Matter Halo via the S2 Star Orbit around Sgr A$^\star$
Derives perihelion shift equations for S2 star in generalized Schwarzschild-Dehnen BH-DM spacetime and constrains gamma, rho_s, rs via MCMC on Do et al. and Gillessen et al. datasets.
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A note on methods for computing the critical curve of Kerr-like black holes
Bardeen's definition of black hole critical curves deviates from de Vries and Grenzebach definitions in homogeneous plasma by contracting with increasing density, contrary to prior expectations.
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Strong-field signatures of a regular black hole in an Einasto dark matter halo
Regular black holes in Einasto dark matter halos show the strongest deviations from Schwarzschild in photon sphere and shadow properties near a critical halo parameter, remaining consistent with Sgr A* but mildly disf...
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Energy conditions in static, spherically symmetric spacetimes and effective geometries
A logarithmic correction to Schwarzschild in static spherical symmetry obeys all classical energy conditions and serves as an effective exterior for horizon-bearing and horizonless compact objects.
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From Ringdown to Lensing: Analytic Eikonal Modes of Quasi-Topological Regular Black Holes
Analytic quasinormal-mode expressions and explicit QNM-shadow-lensing correspondence for four-dimensional quasi-topological regular black holes.
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Observational Tests of Regular Black Holes with Scalar Hair and their Stability
Regular black holes with phantom scalar hair are constrained by Solar System and EHT observations, with exact relations linking photon sphere Lyapunov exponent to shadow size and impact parameter.
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Scalar and Electromagnetic Perturbations around a Black Hole with a Topological Defect: Quasinormal Modes and Quasi-bound States in a Plasma Medium
Plasma and a topological-defect parameter k jointly shift scalar QNM frequencies and permit electromagnetic quasi-bound states only for homogeneous plasma below a critical frequency threshold.
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Detectability of secondary images from flares near Sgr A* with mock GRAVITY data
Bayesian fitting to mock GRAVITY data shows robust detection of secondary images from Sgr A* flares requires both an order-of-magnitude larger sample and astrometric uncertainties reduced to 40% of current levels for ...
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Observational signatures of negative mass wormholes through their shadows
Numerical simulations of negative mass wormholes reveal distinct photon ring substructures in their shadows compared to Schwarzschild black holes and Simpson-Visser wormholes.
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Scalar-Electromagnetic Couplings as Source of Deformed Black Hole: From Shadows to Thermodynamic Topology
A scalar-NED coupled black hole metric is reconstructed from an effective geometry, yielding EHT bounds on magnetic charge, Hawking-Page transition, and topological equivalence to the Reissner-Nordström solution.
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Shadow dependent phenomenology framework for rotating black hole metric
A diffeomorphic inversion re-parameterizes Kerr, Kerr-MOG, and Horndeski black hole observables in terms of the shadow radius, yielding model-specific deflection and luminosity scalings that break mass degeneracy.
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A First-Order Eikonal Framework for Quasinormal Modes, Shadows, Strong Lensing, and Grey-Body Factors in a Scalarized Black-Hole Metric
Derives closed first-order eikonal expressions that connect a scalarized black-hole metric to quasinormal frequencies, shadows, strong deflection, and transmission probabilities.
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A First-Order Eikonal Framework for Quasinormal Modes, Shadows, Strong Lensing, and Grey-Body Factors in a Scalarized Black-Hole Metric
First-order eikonal formulas connect a scalarized black-hole metric to quasinormal modes, shadows, strong lensing, and grey-body factors via photon-sphere invariants in the weak-hair limit.
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On Computational CUDA Studies of Black Hole Shadows
CUDA-based ray tracing shows black hole shadows and emission rates vary with global monopole, charge, and rotation parameters but are insensitive to the Euler-Heisenberg nonlinearity, yielding observational bounds on ...
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ModMax black hole surrounded by perfect-fluid dark matter in Lorentz-violating Kalb-Ramond gravity
Derives static spherically symmetric black hole metric combining ModMax electrodynamics, Lorentz-violating Kalb-Ramond gravity, and perfect-fluid dark matter, then analyzes thermodynamic quantities and stability.
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Constraining Black Hole Parameters in Non-Commutative Geometry using Machine Learning
Machine learning constrains non-commutative black hole parameters and reports consistency with Sgr A* Keck observations.
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Astrophysical environment around a black hole in the braneworld and its optical signatures
Braneworld quadratic and nonlocal corrections weaken gravity in anisotropic Einstein-cluster environments around black holes, blocking horizon formation and shifting Einstein-ring and shadow radii in ways that may con...
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Probing Kalb-Ramond gravity with charged rotating black holes: constraints from EHT observations
EHT shadow observations constrain the Lorentz-violating parameter ℓ in Kalb-Ramond gravity for charged rotating black holes to roughly |ℓ| ≲ 0.1-0.2, with an upper bound ℓ ≲ 0.19 from Sgr A*.
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