Photonic Ring Research Articles

Distinguishing black holes with and without spontaneous scalarization in Einstein-scalar-Gauss–Bonnet theories via optical features

Spontaneous scalarization in Einstein-scalar-Gauss–Bonnet theory admits both vacuum-general relativity (GR) and scalarized hairy black holes as valid solutions, which provides a distinctive signature of new physics in strong gravity regime. In this paper, we shall examine the optical features of Gauss–Bonnet black holes with spontaneous scalarization, which is governed by the coupling parameter λ. We find that the photon sphere, critical impact parameter and innermost stable circular orbit all decrease as the increasing of λ. Using observable data from Event Horizon Telescope, we establish the upper limit for λ. Then we construct the optical appearances of the scalarized black holes illuminated by various thin accretions. Our findings reveal that the scalarized black holes consistently exhibit smaller shadow sizes and reduced brightness compared to Schwarzschild black holes. Notably, in the case of thin spherical accretion, the shadow of the scalarized black hole is smaller, but the surrounding bright ring is more pronounced. Our results highlight the observable features of the scalarized black holes, providing a distinguishable probe from their counterpart in GR in strong gravity regime.

Black Hole and Equipotential Photon Surface Uniqueness in Four-Dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes

AbstractWe study four-dimensional asymptotically flat electrostatic electro-vacuum spacetimes with a connected black hole, photon sphere, or equipotential photon surface inner boundary. Our analysis, inspired by the potential theory approach by Agostiniani–Mazzieri, allows to give self-contained proofs of known uniqueness theorems of the sub-extremal, extremal, and super-extremal Reissner–Nordström spacetimes. We also obtain new results for connected photon spheres and equipotential photon surfaces in the extremal case. Finally, we provide, up to a restriction on the range of their radii, the uniqueness result for connected (both non-degenerate and degenerate) equipotential photon surfaces in the super-extremal case, not yet treated in the literature.

Gravastars as nontopological solitons

We investigate a coupled system consisting of a complex scalar field, a U(1) gauge field, a complex Higgs scalar field, and Einstein gravity. We present nontopological soliton star solutions in which the interior geometry is described by the de Sitter metric, the exterior by the Schwarzschild metric, and these two regions are attached by a spherical surface layer with a finite thickness. This structure is the same as the so-called gravastars, so we refer to these solutions as “solitonic gravastars.” We demonstrate that compact solitonic gravastars that possessing photon spheres can appear. Additionally, we study the mass and compactness of solitonic gravastars for various sets of parameters that characterize the system. Published by the American Physical Society 2024

Phase transitions, shadows, and microstructure of Reissner-Nordström-Anti-de-Sitter black holes from a geometrothermodynamic perspective

We study the thermodynamic properties of the Reissner-Nordström black hole with cosmological constant, expressed in terms of the curvature radius, using the approach of shadow thermodynamics and the formalism of geometrothermodynamics. We derive explicit expressions for the shadow radius in terms of the horizon, photon sphere, and observer radii. The phase transition structure turns out to strongly depend on the value of the curvature radius, including configurations with zero, one, or two phase transitions. We also analyze the black hole's microscopic structure and find differences between the approaches of thermodynamic geometry and geometrothermodynamics, which are due to the presence of the curvature radius. We impose the important condition that the black hole is a quasi-homogeneous thermodynamic system to guarantee the consistency of the geometrothermodynamic approach.

Photon Shells, Black Hole Shadows, and Accretion Toroids

We analyze the properties of the Kerr black hole (BH) photon shell, focusing on the influence of aggregates of corotating and counterrotating toroids (ringed accretion disks, hereafter RAD), orbiting in the BH photon shell (photon shell “obscuration”). The particular case of a corotating accretion disk orbiting in the BH ergoregion is also investigated. We study influence on the BH shadow boundary, fixing the conditions under which it is possible to observe the ergoregion and RAD “imprint” on the shadows boundary. In general, remarkable differences appear between the counterrotating photon components of the boundary with respect to the corotating ones. Various regions of the shadow boundary generated from orbital regions linked to the aggregates of orbiting structures have been analyzed. In particular, we investigate the bound unstable spherical photon orbits in the ergoregion, or at the inversion point, where (toroidal) ϕ̇=0 , or with the impact parameter ℓ = 0 to characterize the effects of the frame dragging on the boundary. Five main classes of BHs have been identified by distinguishable features of their photon shells (and shadow boundaries) in the context of the orbiting RAD.

Modification of Premises for the Black Hole Information Paradox Caused by Topological Constraints in the Event Horizon Vicinity

We demonstrate that at the rim of the photon sphere of a black hole, the quantum statistics transition takes place in any multi-particle system of indistinguishable particles, which passes through this rim to the inside. The related local departure from Pauli exclusion principle restriction causes a decay of the internal structure of collective fermionic systems, including the collapse of Fermi spheres in compressed matter. The Fermi sphere decay is associated with the emission of electromagnetic radiation, taking away the energy and entropy of the falling matter without unitarity violation. The spectrum and timing of the related e-m radiation agree with some observed short giant gamma-ray bursts and X-ray components of the luminosity of quasars and of short transients powered by black holes. The release of energy and entropy when passing the photon sphere rim of a black hole significantly modifies the premises of the information paradox at the falling of matter into a black hole.

Is a photon ring invariably a closed structure?

In this study, we investigate the image of a rotating compact object (CO) illuminated by a geometrically thin, optically thin disk on the equatorial plane. As the radius of the CO’s surface fluctuates, the CO may partially or entirely obscure the photon region. We observe that the perceived photon ring may exhibit discontinuities, deviating from a closed structure, and may even disappear entirely. We find that the disruption and disappearance of the photon ring are dependent on the observational angle-a novel phenomenon not previously observed in black hole imaging studies. Our study reveals that while the factors influencing this unique photon ring phenomenon are diverse and the outcomes complex, we can provide a clear and comprehensive explanation of the physical essence and variation trends of this phenomenon. We do this by introducing and analyzing the properties and interrelationships of three characteristic functions, η~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ilde{\\eta }$$\\end{document}, ηo\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta _o$$\\end{document}, and ηs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta _s$$\\end{document} related to the photon impact parameters. Additionally, our analysis of the intensity cuts and inner shadows of the images uncovers patterns that differ significantly from the shadow curve.

Photon rings in the metamaterial analog of a gravitomagnetic monopole

Photon rings in the metamaterial analog of a gravitomagnetic monopole

Plasma impact on black hole shadows and gravitational weak lensing in the Einstein–Maxwell-scalar theory

In this paper, we investigate the optical properties of a non-rotating charged black hole (BH) in the Einstein–Maxwell-scalar (EMS) theory, together with a plasma medium. We first consider the photon sphere and shadow radius under the impact of the plasma medium existing in the environment surrounding the BH in the EMS theory. We show that the radius of the photon sphere and the BH shadow decrease under the influence of the parameter β. We further study gravitational weak lensing in detail by adapting general methods and derive the light ray’s deflection angle around the BH together with the plasma environment. It is found that for uniform plasma, the deflection angle increases with the rise of the plasma parameter, whereas it decreases with the increase of the plasma parameter for non-uniform plasma. Besides, we also study the magnification of image brightness.

Analyzing the Influence of Geometrical Deformation on Photon Sphere and Shadow Radius: A New Analytical Approach -Stationary, and Axisymmetric Spacetime

Analyzing the Influence of Geometrical Deformation on Photon Sphere and Shadow Radius: A New Analytical Approach -Stationary, and Axisymmetric Spacetime

Relativistic reflection modeling in AGN and related variability from PCA: a brief review

X-ray observations of active galactic nuclei (AGNs) reveal relativistic reflections from the innermost regions of accretion disks, which contain general-relativistic footprints caused by spinning supermassive black holes (SMBH). We anticipate the spin of a SMBH to be stable over the human timeframe, so brightness changes in the high-energy corona above the SMBH should slightly alter relativistic reflection. In this brief review, we discuss the latest developments in modeling relativistic reflection, as well as the rapid small variation in relativistic emission disclosed by the principal component analysis (PCA) of X-ray variability in AGN. PCA studies of X-ray spectra from AGNs have shown that relativistically blurred reflection has negligible fluctuations over the course of observations, which could originate from rapid (intrahour) intrinsic variations in near-horizon accretion flows and photon rings. The PCA technique is an effective way to disclose relativistic reflection from X-ray observations of AGNs, simplifying the complexity of largely variable X-ray data for automated spectral analysis with machine learning algorithms.

Black holes, photon sphere, and cosmology in ghost-free [formula omitted] gravity

The improved version of ghost-free f(G) gravity introduced in Nojiri and Odintsov (2005) is proposed and investigated. It is demonstrated that improved ghost-free f(G) gravity may be consistently applied to describe the expanding universe (with horizon) as well as the static spacetime like black holes. Interestingly, such a theory looks like a close avatar of scalar-Einstein–Gauss–Bonnet gravity with the only difference that the scalar field is not a dynamical one so that many predictions of ghost-free f(G) gravity are very similar to that of sEGB gravity.We discuss the gravitational wave in the improved model with the condition that the propagating speed of the gravitational wave is identical to that of the propagation speed of light. A model that describes inflation in the early universe and could satisfy the observational constraints is also constructed. The solution of ghost-free f(G) gravity realising the given static spacetime with spherical symmetry is proposed. Some of such solutions realise explicitly the Reissner–Nordström black hole or the Hayward black hole, which is a regular black hole without curvature singularity, We also construct a black hole in our theory which contains the Arnowitt–Deser–Misner (ADM) mass, the horizon radius, and the radius of the photon sphere as independent parameters. The radius of the black hole shadow in this model as well as photon sphere radius are estimated. It is shown that there exists a parameter region which satisfies the constraints coming from Event Horizon Telescope observations. Furthermore, we construct model where the radius of the black hole shadow or photon orbit is smaller than the horizon radius supposed from the ADM mass.

Loosely Trapped Surface for Slowly Rotating Black Hole

Abstract We construct the marginal loosely trapped surface (marginal LTS) for the Kerr spacetime with a small Kerr parameter perturbatively, where the LTS condition is saturated. An LTS is a surface that specifies the strong gravity region, which is a generalization of the photon sphere in the Schwarzschild spacetime. It turns out that there are an infinite number of marginal LTSs. At the leading order of the small Kerr parameter, all of the marginal LTSs have the same area. However, one can see that the maximal marginal LTS among them is uniquely determined at the higher order.

A new class of traversable wormhole metrics

In this work, we have formulated a new class of traversable wormhole metrics. Initially, we have considered a wormhole metric in which the temporal component is an exponential function of r but the spatial components of the metrics are fixed. Following that, we have again constructed a generalized wormhole metric in which the spatial component is an exponential function of r, but the temporal component is fixed. Finally, we have considered the generalized wormhole metric in which both the temporal and spatial components are generalized exponential functions of r. We have also studied some of their properties including throat radius, stability, and energy conditions, examined singularity, the metric in curvature coordinates, effective refractive index, innermost stable circular orbit (ISCO) and photon sphere, Regge–Wheeler potential and their quasinormal modes, gravitational entropy, and determined the curvature tensor. The radius of the throat is found to be consistent with the properties of wormholes and does not contain any types of singularities. Most interestingly, we find that their throat radius is the same for the same spatial component and the same range of values of m. In addition to these, they also violate the Null Energy Condition (NEC) near the throat. These newly constructed metrics form a new class of traversable wormholes.

Horizon replicas in black hole shadows

Recently, new exploratory channels have opened up for the physics of highly compact objects, such as gravitational waves and black hole shadows. Moreover, more precise analysis and observations are now possible in the physics of accretion around compact objects. These advancements provide in particular an unprecedented insight into the physics near the horizons of a black hole. In this work we focus on the shadow boundary of a Kerr black hole, introducing observables related to special null orbits, called horizons replicas, solutions of the shadow edge equations which are related to particular photon orbits, defined by constraints on their impact parameter, carrying information about the angular momentum of the central spinning object. These orbits are related to particular regions on the shadow boundary and might be used to determine the spin of the black hole. The results provide the conditions by which horizon replicas are imprinted in the black hole shadow profile, in dependence on the black hole dimensionless spin and observational angle, providing eventually new templates for the future observations.

Thermodynamics and null geodesics of a Schwarzschild black hole surrounded by a Dehnen type dark matter halo

In this work, we derive a novel black hole solution surrounded by a Dehnen-(1,4,0) type dark matter halo by embedding a Schwarzschild black hole within the halo, constituting a composite dark matter-black hole system. The thermodynamics of the resulting effective black hole spacetime is then studied with particular attention to the influence of the dark matter parameters on various thermodynamic properties. We examine the specific heat and free energy to assess the thermodynamic stability of the model. Furthermore, the null geodesics and the effective potential of light rays are studied to investigate how the dark matter parameters affect these geodesics and the radii of circular orbits. The stability of circular null geodesics is analysed using dynamical systems and Lyapunov exponents, which represent the dynamical behaviour of the circular photon orbits. Finally, we studied if the circular geodesics exhibit chaotic behaviour using the chaos-bound condition.

Orbital Precession in Janis–Newman–Winicour Spacetime

We have investigated the Janis–Newman–Winicour spacetime through three fundamental tests of theories of gravity, namely, gravitational lensing, perihelion shift, and redshift due to gravitational force. Focusing initially on the circular motion of a massive particle within the equatorial plane, the analysis disregards external scalar field interactions. The Janis–Newman–Winicour (JNW) spacetime’s unique parameters, mass (M) and the scalar parameter (n), are examined, revealing an intriguing relationship between the innermost stable circular orbit position of the test particle and the scalar field parameter. The study also explores photon motion around a gravitational object in JNW spacetime, revealing the expansion of the photon sphere alongside a diminishing shadow, influenced by the external scalar field. Despite these complexities, gravitational bending of light remains consistent with general relativity predictions. The investigation extends to perihelion precession, where the trajectory of a massive particle in JNW spacetime exhibits eccentricity-dependent shifts, distinguishing it from Schwarzschild spacetime. Finally, oscillatory motion of massive particles in JNW spacetime is explored, providing analytical expressions for epicyclic frequencies using perturbation methods. The study concludes with the application of MCMC analyses to constrain the JNW spacetime parameters based on observational data.

Exploring the possibility of testing the no-hair theorem with Minkowski-deformed regular hairy black holes via photon rings

In this paper, we investigate the optical appearance of a regular static spherically symmetric hairy black hole within the context of Minkowski deformation governed by the parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. This black hole describes a hairy black hole with geometric deformations in the radial and temporal metric components, parameterized by α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. The optical appearance of the black hole, illuminated by a static thin accretion disk in three toy emission function models, exhibits distinctive shadows and photon rings. Our findings reveal that for static spherically symmetric hairy Minkowski-deformed regular black holes, the event horizon radius rh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_h$$\\end{document}, photon sphere radius rph\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{ph}$$\\end{document}, critical impact parameter bph\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b_{ph}$$\\end{document}, and innermost stable circular orbit radius risco\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{isco}$$\\end{document} all have a positive correlation with α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. These parameters affect the null geodesic trajectories, shadows, and the optical appearance of the photon rings illuminated by a static thin accretion disk around the black hole. Utilizing this, we obtained the optical appearance of this black hole when observed in the forward direction of the optical and geometric thin accretion disk models. In all three models, the radius of the photon ring images also shows a positive correlation with the parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. Therefore, under the static spherically symmetric hairy Minkowski-deformed regular black hole, there is no degeneracy of photon rings dependent on the parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. Theoretically, this allows for the distinction of different spacetime metrics of hairy Minkowski-deformed regular black holes, providing a potential method for testing the no-hair theorem through future observations of black hole photon rings.

Explanation for the Absence of Secondary Peaks in Black Hole Light Curve Autocorrelations.

The observed radiation from hot gas accreting onto a black hole depends on both the details of the flow and the spacetime geometry. The lensing behavior of a black hole produces a distinctive pattern of autocorrelations within its photon ring that encodes its mass, spin, and inclination. In particular, the time autocorrelation of the light curve is expected to display a series of peaks produced by light echoes of the source, with each peak delayed by the characteristic time lapse τ between light echoes. However, such peaks are absent from the light curves of observed black holes. Here, we develop an analytical model for such light curves that demonstrates how, even though light echoes always exist in the signal, they do not produce autocorrelation peaks if the characteristic correlation timescale λ_{0} of the source is greater than τ. We validate our model against simulated light curves of a stochastic accretion model ray traced with a general-relativistic code, and then fit the model to an observed light curve for Sgr A^{*}. We infer that λ_{0}>τ, providing an explanation for the absence of light echoes in the time autocorrelations of Sgr A^{*} light curves. Our results highlight the importance for black hole parameter inference of spatially resolving the photon ring via future space-based interferometry.

Quasinormal modes, thermodynamics and shadow of black holes in Hu–Sawicki f(R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{f(R)}$$\\end{document} gravity theory

We derive novel black hole solutions in a modified gravity theory, namely the Hu–Sawicki model of f(R) gravity. After obtaining the black hole solution, we study the horizon radius of the black hole from the metric and then analyse the dependence of the model parameters on the horizon. We then use the 6th order WKB method to study the quasinormal modes of oscillations (QNMs) of the black hole perturbed by a scalar field. The dependence of the amplitude and damping part of the QNMs are analysed with respect to variations in model parameters and the error associated with the QNMs are also computed. After that we study some thermodynamic properties associated with the black hole such as its thermodynamic temperature as well as greybody factors. It is found that the black hole has the possibility of showcasing negative temperatures and is thermodynamically unstable for feasible values of model parameters. Then we analyse the geodesics and derive the photon sphere radius as well as the shadow radius of the black hole. The photon radius is independent of the model parameters while shadow radius showed fair amount of dependence on the model parameters. We tried to constrain the parameters with the help of Keck and VLTI observational data and obtained some bounds on m and c2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_{2}$$\\end{document} parameters.