Quasinormal modes-shadow correspondence for rotating regular black holes

Abstract

Eikonal quasinormal modes (QNMs) of black holes (BHs) and parameters of null geodesics, ultimately tied to the appearance of BHs to external observers, are known to be related, and the eikonal QNM-BH shadow radii correspondence has been extensively studied for spherically symmetric BHs. The extension to rotating BHs is non-trivial, and has been worked out only for equatorial ($m=\pm \ell$) QNMs, or for general modes but limited to the Kerr metric. We extend the QNM-shadow radius correspondence to more general rotating space-times, and argue that the requirements for it to hold amount to conditions on the separability of the Hamilton-Jacobi equation for null geodesics and the Klein-Gordon equation. Metrics obtained by the Newman-Janis algorithm enjoy these conditions, provided certain mathematical requirements are imposed on the line element. We explicitly verify the correspondence for the rotating Bardeen and Hayward regular BHs, both of which satisfy the separability requirements. Our findings show that the QNM-shadow radius correspondence holds for a wide range of axisymmetric space-times beyond Kerr. This paves the way to potential strong-field multi-messenger tests of fundamental physics by hearing (via gravitational wave spectroscopy) and seeing (via VLBI imaging) BHs, although substantial improvements relative to the current observational sensitivity are required to make this possible.

arXiv comment21 pages, 6 sub-figures arranged into 4 figures. v2: several additional references added, minor change to title (which unfortunately lost its cool first part!), minor changes to Figures. v3: removed spurious references to lightnings and thunders in abstract and main text to reflect published version, removed duplicate reference. Version published in PRD

References in corpus (246)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Quasinormal modes of black holes and black branes
• Quasi-Normal Modes of Stars and Black Holes
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run
• Quasinormal modes of black holes: from astrophysics to string theory
• Testing General Relativity with Present and Future Astrophysical Observations
• Formation and evaporation of non-singular black holes
• Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics
• Viewing the Shadow of the Black Hole at the Galactic Center
• Schwarzschild black hole lensing
• Geodesic stability, Lyapunov exponents and quasinormal modes
• Dark Energy after GW170817: dead ends and the road ahead
• Testing the nature of dark compact objects: a status report
• The Bardeen Model as a Nonlinear Magnetic Monopole
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Dark Energy after GW170817 and GRB170817A
• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• Black holes, gravitational waves and fundamental physics: a roadmap
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• Calculating black hole shadows: Review of analytical studies
• Noncommutative Black Holes, The Final Appeal To Quantum Gravity: A Review
• Tests of General Relativity with GW170817
• New Regular Black Hole Solution from Nonlinear Electrodynamics
• Shadows and strong gravitational lensing: a brief review
• Science with the space-based interferometer eLISA. I: Supermassive black hole binaries
• Rotating regular black holes
• Testing the rotational nature of the supermassive object M87* from the circularity and size of its first image
• Jerusalem Lectures on Black Holes and Quantum Information
• Construction of Regular Black Holes in General Relativity
• Regular phantom black holes
• Shadow of rotating regular black holes
• Generating rotating regular black hole solutions without complexification
• Universal Interferometric Signatures of a Black Hole's Photon Ring
• Hunting for extra dimensions in the shadow of M87*
• Constraints on black-hole charges with the 2017 EHT observations of M87*
• Are eikonal quasinormal modes linked to the unstable circular null geodesics?
• Black hole evaporation: A paradigm
• Magnetically charged black holes from non-linear electrodynamics and the Event Horizon Telescope
• Singularity Theorems and Their Consequences
• Nonlinear electrodynamics effects on the black hole shadow, deflection angle, quasinormal modes and greybody factors
• Black holes with non-minimal derivative coupling
• Black holes with scalar hair in light of the Event Horizon Telescope
• Rotating black holes in $4D$ Einstein-Gauss-Bonnet gravity and its shadow
• Regular Black Holes and Topology Change
• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• Black hole shadow in an asymptotically-flat, stationary, and axisymmetric spacetime: The Kerr-Newman and rotating regular black holes
• Regular Black Hole Metric with Three Constants of Motion
• The 1965 Penrose singularity theorem
• The Shadow of a Spherically Accreting Black Hole
• Instabilities of wormholes and regular black holes supported by a phantom scalar field
• Quasinormal-mode spectrum of Kerr black holes and its geometric interpretation
• Parameter estimation of hairy Kerr black holes from its shadow and constraints from M87*
• Constraining the spin and the deformation parameters from the black hole shadow
• Four Parametric Regular Black Hole Solution
• Kerr Black Holes as Elementary Particles
• Black holes in an ultraviolet complete quantum gravity
• Silhouette of M87*: A new window to peek into the world of hidden dimensions
• Connection between black-hole quasinormal modes and lensing in the strong deflection limit
• Shadow and Quasinormal Modes of a Rotating Loop Quantum Black Hole
• 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
• GW170817 Falsifies Dark Matter Emulators
• Regular black holes: A short topic review
• Regular black holes in quadratic gravity
• Swampland Implications of GW170817-compatible Einstein-Gauss-Bonnet Gravity
• On the viability of regular black holes
• Shadow cast and deflection of light by charged rotating regular black holes
• Shadow, lensing, quasinormal modes, greybody bounds and neutrino propagation by dyonic ModMax black holes
• Geodesically complete black holes
• Shadows and deflection angle of charged and slowly rotating black holes in Einstein-Æther theory
• A novel family of rotating black hole mimickers
• The Gravitational-Wave Physics
• From static to rotating to conformal static solutions: Rotating imperfect fluid wormholes with(out) electric or magnetic field
• An explanation of the Newman-Janis Algorithm
• Mining information from binary black hole mergers: a comparison of estimation methods for complex exponentials in noise
• Generic rotating regular black holes in general relativity coupled to nonlinear electrodynamics
• Static spherically symmetric solutions in mimetic gravity: rotation curves & wormholes
• Quasinormal Modes of Black Holes Surrounded by Dark Matter and Their Connection with the Shadow Radius
• Post-Newtonian Evolution of Massive Black Hole Triplets in Galactic Nuclei: IV. Implications for LISA
• Concerns regarding the use of black hole shadows as standard rulers
• Field sources for Simpson-Visser space-times
• Vainshtein mechanism after GW170817
• Shadows and gravitational weak lensing by the Schwarzschild black hole in the string cloud background with quintessential field
• Brane-world extra dimensions in light of GW170817
• Constraints on Einstein-aether theory after GW170817
• Quasinormal modes, quasiperiodic oscillations and shadow of rotating regular black holes in non-minimally coupled Einstein-Yang-Mills theory
• Photon Ring and Observational Appearance of a Hairy Black Hole
• Superradiance evolution of black hole shadows revisited
• Formation Rate of Extreme Mass Ratio Inspirals in Active Galactic Nuclei
• $f(T)$ gravity after GW170817 and GRB170817A
• Tests of Loop Quantum Gravity from the Event Horizon Telescope Results of Sgr A${}^{\ast }$
• Strong gravitational lensing and shadow constraint from M87* of slowly rotating Kerr-like black hole
• EHT constraint on the ultralight scalar hair of the M87 supermassive black hole
• Circular geodesics of Bardeen and Ayon-Beato-Garcia regular black-hole and no-horizon spacetimes
• Asymptotic safety casts its shadow
• Resolving Spacetime Singularities within Asymptotic Safety
• The fate of large-scale structure in modified gravity after GW170817 and GRB170817A
• Constraining a modified gravity theory in strong gravitational lensing and black hole shadow observations
• No-Hair Theorem in the Wake of Event Horizon Telescope
• Astrophysical Black Holes: A Compact Pedagogical Review
• Photon Spheres and Spherical Accretion Image of a Hairy Black Hole
• Quantum Corrected Black Holes from String T-Duality
• The Quasinormal Mode Spectrum of a Kerr Black Hole in the Eikonal Limit
• Vainshtein Screening in Scalar-Tensor Theories before and after GW170817: Constraints on Theories beyond Horndeski
• Imprints of Dark Matter on Black Hole Shadows using Spherical Accretions
• Testing dynamical torsion effects on the charged black hole's shadow, deflection angle and greybody with M87* and Sgr. A* from EHT
• Black-hole quasinormal resonances: Wave analysis versus a geometric-optics approximation
• Testing Rotating Regular Metrics as Candidates for Astrophysical Black Holes
• Nonlinear electrodynamics, regular black holes and wormholes
• Quasinormal ringing of regular black holes in asymptotically safe gravity: the importance of overtones
• Testing Rotating Regular Metrics with EHT Results of Sgr A*
• Alive and well: mimetic gravity and a higher-order extension in light of GW170817
• Inner horizon instability and the unstable cores of regular black holes
• Connection Between the Shadow Radius and Quasinormal Modes in Rotating Spacetimes
• Mimicking dark matter and dark energy in a mimetic model compatible with GW170817
• Shadows and photon rings of regular black holes and geonic horizonless compact objects
• Stability of a vacuum nonsingular black hole
• Further clarification on quasinormal modes/circular null geodesics correspondence
• A worldsheet for Kerr
• Shadow and weak deflection angle of extended uncertainty principle black hole surrounded with dark matter
• Einstein-Æther Gravity in the light of Event Horizon Telescope Observations of M87*
• Regular black holes with stable cores
• Dynamics of Scalar Fields in the Background of Rotating Black Holes
• Analytical correspondence between shadow radius and black hole quasinormal frequencies
• Shadow, quasinormal modes and quasiperiodic oscillations of rotating Kaluza-Klein black holes
• Superradiant evolution of the shadow and photon ring of Sgr A${}^{\star }$
• Black hole scalarization induced by the spin -- 2+1 time evolution
• Hayward black holes in Einstein-Gauss-Bonnet gravity
• Shadow, deflection angle and quasinormal modes of Born-Infeld charged black holes
• Shadow and quasinormal modes of the Kerr-Newman-Kiselev-Letelier black hole
• Janis-Newman algorithm: generating rotating and NUT charged black holes
• Black Hole Ringing, Quasinormal Modes, and Light Rings
• EHT tests of the strong-field regime of General Relativity
• Investigating the Connection between Generalized Uncertainty Principle and Asymptotically Safe Gravity in Black Hole Signatures through Shadow and Quasinormal Modes
• Eikonal quasinormal modes of black holes beyond General Relativity
• Testing Symmergent gravity through the shadow image and weak field photon deflection by a rotating black hole using the M87${}^{\ast }$ and Sgr. A${}^{\ast }$ results
• Probing the Lorentz Symmetry Violation Using the First Image of Sagittarius A*: Constraints on Standard-Model Extension Coefficients
• An Upper Limit on the Charge of the Black Hole Sgr A* from EHT Observations
• From a locality-principle for new physics to image features of regular spinning black holes with disks
• Non-Minimally Coupled Einstein Gauss Bonnet Inflation Phenomenology in View of GW170817
• Black hole shadow as a standard ruler in cosmology
• Regularized Stable Kerr Black Hole: Cosmic Censorships, Shadow and Quasi-Normal Modes
• The physics of the relativistic counter-streaming instability that drives mass inflation inside black holes
• Black holes in Starobinsky-Bel-Robinson Gravity and the breakdown of quasinormal modes/null geodesics correspondence
• Quasinormal Modes of Black Holes with Multiple Photon Spheres
• Constraints on Barrow entropy from M87* and S2 star observations
• Thermodynamics and Shadows of GUP-corrected Black Holes with Topological Defects in Bumblebee Gravity
• Quasinormal modes of charged black holes with corrections from nonlinear electrodynamics
• Geodesic incompleteness of some popular regular black holes
• Weak gravitational lensing and shadow of a GUP-modified Schwarzschild black hole in the presence of plasma
• Probing Schwarzschild-like Black Holes in Metric-Affine Bumblebee Gravity with Accretion Disk, Deflection Angle, Greybody Bounds, and Neutrino Propagation
• Kerr black holes with synchronised Proca hair: lensing, shadows and EHT constraints
• Analytic expressions for quasinormal modes and grey-body factors in the eikonal limit and beyond
• Quasinormal modes, shadow and greybody factors of 5D electrically charged Bardeen black holes
• Probing the Nature of Black Holes: Deep in the mHz Gravitational-Wave Sky
• Eikonal quasinormal modes and shadow of string-corrected $d$-dimensional black holes
• Relating Black Hole Shadow to Quasinormal Modes for Rotating Black Holes
• A review on analytical studies in Gravitational Lensing
• Regular black holes in UV self-complete quantum gravity
• Analytical quasinormal modes of spherically symmetric black holes in the eikonal regime
• Black hole solutions in massive gravity
• Non-polynomial Lagrangian approach to Regular Black Holes
• Regular Black Holes: Towards a New Paradigm of Gravitational Collapse
• Complex angular momentum in black hole physics and quasinormal modes
• Testing black hole mimickers with the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Rotating black holes in general relativity coupled to nonlinear electrodynamics
• Photon rings as tests for alternative spherically symmetric geometries with thin accretion disks
• A note on singular and non-singular black holes
• Upper bound on the GUP parameter using the black hole shadow
• Rotating black holes without ${\mathbb{Z}}_2$ symmetry and their shadow images
• No firewalls in quantum gravity: the role of discreteness of quantum geometry in resolving the information loss paradox
• Correspondence of eikonal quasinormal modes and unstable fundamental photon orbits for Kerr-Newman black hole
• Eikonal black hole ringings in generalized energy-momentum squared gravity
• Regular evaporating black holes with stable cores
• Eikonal quasinormal modes of black holes beyond general relativity III: scalar Gauss-Bonnet gravity
• Eikonal quasinormal modes of black holes beyond general relativity II: generalised scalar-tensor perturbations
• Bardeen regular black hole as a quantum-corrected Schwarzschild black hole
• Self force via $m$-mode regularization and 2+1D evolution: II. Scalar-field implementation on Kerr spacetime
• Asymptotically locally flat and AdS higher-dimensional black holes of Einstein-Horndeski-Maxwell gravity in the light of EHT observations: shadow behavior and deflection angle
• Charged black-bounce spacetimes: Photon rings, shadows and observational appearances
• Chaotic Shadows of Black Holes: A Short Review
• Spin-induced scalarization of Kerr black holes with a massive scalar field
• Classical mass inflation vs semiclassical inner horizon inflation
• Object picture of scalar field perturbation on Kerr black hole in scalar-Einstein-Gauss-Bonnet theory
• Observational constraints on Yukawa cosmology and connection with black hole shadows
• Mode coupling mechanism for late-time Kerr tails
• Quasinormal modes and greybody factors of symmergent black hole
• Dissimilar Donuts in the Sky? Effects of a Pressure Singularity on the Circular Photon Orbits and Shadow of a Cosmological Black Hole
• Remarks on non-singular black holes
• Quasinormal modes and shadows of a new family of Ayón-Beato-Garc\'ıa black holes
• Physical Properties of a Regular Rotating Black Hole: Thermodynamics, Stability, Quasinormal Modes
• Null geodesics, quasinormal modes, and thermodynamic phase transition for charged black holes in asymptotically flat and dS spacetimes
• Lessons from black hole quasinormal modes in modified gravity
• Observational Appearances of Magnetically Charged Black Holes in Born-Infeld Electrodynamics
• The Galactic Center as a laboratory for theories of gravity and dark matter
• Correspondence between quasinormal modes and the shadow radius in a wormhole spacetime
• Echoes from Hairy Black Holes
• A new cosmological probe using super-massive black hole shadows
• The shadow of regular black holes with asymptotically Minkowski core
• The high energy universe at ultra-high resolution: the power and promise of X-ray interferometry
• EHT observables as a tool to estimate parameters of supermassive black holes
• Bottom-Up Reconstruction of Viable GW170817 Compatible Einstein-Gauss-Bonnet Theories
• Null geodesics, quasinormal modes and the correspondence with shadows in high-dimensional Einstein-Yang-Mills spacetimes
• Eikonal quasinormal modes and photon orbits of deformed Schwarzschild black holes
• Remarks on nonsingular models of Hayward and magnetized black hole with rational nonlinear electrodynamics
• Constraining the Generalized Uncertainty Principle Through Black Hole Shadow and Quasiperiodic Oscillations
• Regular black holes, universes without singularities, and phantom-scalar field transitions
• Quasinormal Modes and Optical Properties of 4-D black holes in Einstein Power-Yang-Mills Gravity
• Horizonless spacetimes as seen by present and next-generation Event Horizon Telescope arrays
• Signatures of regular black holes from the shadow of Sgr A* and M87*
• Lifetime of scalar cloud formation around a rotating regular black hole
• Anisotropic Generalized Polytropic Spheres: Regular 3D Black Holes
• Observational Signatures: Shadow cast by the effective metric of photons for black holes with rational non-linear electrodynamics
• Implications of axionic hair on shadow of M87*
• Signatures of the accelerating black holes with a cosmological constant from the ${\text{Sgr A}}^{\star }$ and ${\text{M87}}^{\star }$ shadow prospects
• A novel test of gravity via black hole eikonal correspondence
• Non-Singular Black Holes and mass inflation in modified gravity
• Separability of the Klein-Gordon equation for rotating spacetimes obtained from Newman-Janis algorithm
• Qualifying ringdown and shadow of black holes under general parametrized metrics with photon orbits
• Probing the Big Bang with quantum fields
• Comment on "Regular evaporating black holes with stable cores"
• Cartesian Kerr-Schild variation on the Newman-Janis ansatz
• Note on fundamental physics tests from black hole imaging: Comment on "Hunting for extra dimensions in the shadow of Sagittarius A${}^{\ast }$"
• Massive scalar field perturbation on Kerr black holes in dynamical Chern-Simons gravity
• Rotating Black Hole in Kalb-Ramond Gravity: Constraining Parameters by Comparison with EHT Observations of Sgr A* and M87*
• Newman-Janis algorithm's application to regular black hole models
• Regular black holes in Verlinde's emergent gravity
• Astrodynamical middle-frequency interferometric gravitational wave observatory AMIGO: Mission concept and orbit design
• Deflection angle, quasinormal modes and optical properties of a de Sitter black hole in $f(\mathcal{T},\mathcal{B})$ gravity
• Regular solutions for black strings and torus-like black holes
• Connections between the shadow radius and the quasinormal modes of Kerr-Sen black hole
• High-dimensional Schwarzschild black holes in scalar-tensor-vector gravity theory
• Optical features of AdS black holes in the novel 4D Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics
• Constraint on the radius of five-dimensional dS spacetime with GW170817 and GRB 170817A
• Quasinormal Modes of the Generalized Ayón-Beato-Garc\'ıa Scalar-Tensor-Vector Gravity Black Hole in the Scalar-Tensor-Vector Gravity
• Quasinormal modes and the correspondence with shadow in black holes with a deficit solid angle and quintessence-like matter
• Constraining a one-dimensional wave-type gravitational wave parameter through the shadow of M87* via Event Horizon Telescope
• Shadows and quasinormal modes of a charged non-commutative black hole by different methods
• Null Geodesics and QNMs in the field of Regular Black Holes
• Lagrangian reverse engineering for regular black holes
• Viable wormhole solution in Bopp-Podolsky electrodynamics
• Double shadow of a 4D Einstein-Gauss-Bonnet black hole and their connection between with quasinormal modes
• Reply to "Comment" on "Regular evaporating black holes with stable cores"
• Observational features of reflection asymmetric black holes

Cited by in corpus (18)

• Primordial regular black holes as all the dark matter. II. Non-time-radial-symmetric and loop quantum gravity-inspired metrics
• Primordial regular black holes as all the dark matter. I. Time-radial-symmetric metrics
• Perturbations and Quasinormal Modes of the Dirac Field in Effective Quantum Gravity
• Trinity of black hole correspondences: Shadows, quasinormal modes, graybody factors, and cautionary remarks
• Importance of being nonminimally coupled: Scalar Hawking radiation from regular black holes
• Properties of an axisymmetric Lorentzian non-commutative black hole
• Topological regular black holes without Cauchy horizon
• Primordial regular black holes as all the dark matter. III. Covariant canonical quantum gravity models
• Can light-rings self-gravitate?
• Grey-body factors of higher dimensional regular black holes in quasi-topological theories
• Scalar Quasinormal Modes of Rotating Regular Black Holes
• Black holes surrounded by massive vector fields in Kaluza-Klein gravity
• Constraining the rotating Simpson-Visser spacetime from the observed quasi-periodic oscillations in black holes
• Shadows of a Non-Commutative Black Hole under the Influence of a Magnetized Plasma
• Ringing Regularity: Gravitational Perturbations and Quasinormal Modes of Einasto-Supported Black Holes
• Confronting eikonal and post-Kerr methods with numerical evolution of scalar field perturbations in spacetimes beyond Kerr
• Black holes and wormholes in Deser-Woodard gravity
• Internal structure of Hayward black holes