In the rotating García-Díaz NLED black hole the Fresnel quartic factorizes into two optical metrics whose critical families project to distinct contours Γ+ and Γ- whose angular separation is generated by the constitutive response and redistributed by spin.
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Perlick,Calculating black hole shadows: Review of analytical studies,Phys
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abstract
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.
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representative citing papers
Soft-haired Kerr black holes show rotated, dilated, drifting images and an image memory effect when soft hair changes via waves, with the effect scaling with the large black hole's mass and spin.
Regular Vaidya solutions exist in effective gravitational theories that dynamically describe radiation-driven formation of regular black holes or mimickers without curvature singularities.
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.
Torn accretion disks around Kerr black holes erode the inner shadow and produce bifurcated, crescent, and multi-order ring morphologies hard to obtain with standard equatorial disks.
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.
Rotating wormhole shadows develop cusps above a universal critical redshift value λ_c, yielding four morphologies: smooth, cuspy, ears touching, and throat drowning.
EHT dimensionless shadow diameters plus stellar-dynamical mass priors constrain Einasto central density to ρ₀ ≲ 10^{-11} M⊙/pc³ (1σ) for Sgr A*, with weaker bounds for M87*.
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 parameters.
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.
Positive/negative-mass binaries would emit gravitational waves with decreasing frequency and amplitude, and a negative-mass wormhole would cast an asymmetric shadow with richer photon-ring substructure than a black hole.
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.
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 disfavoring M87* at high values.
A constructive algorithm yields NEC-obeying static spherical metrics with g_tt g_rr = -1, including a log-corrected Schwarzschild geometry that can mimic black holes.
Analytic quasinormal-mode expressions and explicit QNM-shadow-lensing correspondence for four-dimensional quasi-topological regular black holes.
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.
Plasma and topological defect k suppress scalar QNM frequencies and allow axial EM quasi-bound states only for homogeneous plasma below a k- and l-dependent critical frequency.
Increasing zero-point length makes photon and ISCO orbits more compact in ADM units while heavier scalars raise oscillation frequency and suppress damping on this regular self-energy black hole.
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 |ΔBIC| > 7.9.
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.
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.
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.
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 those three quantities.
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.
citing papers explorer
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Constitutive birefringence and critical curves in the rotating Garc\'ia--D\'iaz black hole
In the rotating García-Díaz NLED black hole the Fresnel quartic factorizes into two optical metrics whose critical families project to distinct contours Γ+ and Γ- whose angular separation is generated by the constitutive response and redistributed by spin.
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Shaving off soft hairs and the black hole image memory effect
Soft-haired Kerr black holes show rotated, dilated, drifting images and an image memory effect when soft hair changes via waves, with the effect scaling with the large black hole's mass and spin.
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Regular Vaidya solutions of effective gravitational theories
Regular Vaidya solutions exist in effective gravitational theories that dynamically describe radiation-driven formation of regular black holes or mimickers without curvature singularities.
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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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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 produce bifurcated, crescent, and multi-order ring morphologies hard to obtain with standard equatorial disks.
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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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Observational Limits on Einasto Dark Matter Parameters from Event Horizon Telescope Images of Sgr A$^{*}$ and M87$^{*}$
EHT dimensionless shadow diameters plus stellar-dynamical mass priors constrain Einasto central density to ρ₀ ≲ 10^{-11} M⊙/pc³ (1σ) for Sgr A*, with weaker bounds for M87*.
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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 parameters.
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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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Observational signatures of negative mass wormholes through their shadows
Positive/negative-mass binaries would emit gravitational waves with decreasing frequency and amplitude, and a negative-mass wormhole would cast an asymmetric shadow with richer photon-ring substructure than a black hole.
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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 disfavoring M87* at high values.
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Energy conditions in static, spherically symmetric spacetimes and effective geometries
A constructive algorithm yields NEC-obeying static spherical metrics with g_tt g_rr = -1, including a log-corrected Schwarzschild geometry that can mimic black holes.
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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 topological defect k suppress scalar QNM frequencies and allow axial EM quasi-bound states only for homogeneous plasma below a k- and l-dependent critical frequency.
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Wave and particle probes of a regular T-duality-inspired black hole with gravitational self-energy
Increasing zero-point length makes photon and ISCO orbits more compact in ADM units while heavier scalars raise oscillation frequency and suppress damping on this regular self-energy black hole.
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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 |ΔBIC| > 7.9.
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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
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 those three quantities.
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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 constrain brane tension for sub-stellar-mass objects.
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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*.
- Higher-Derivative Corrections to Reissner--Nordstr\"om Black Holes from Worldline QFT