Photonic Ring Research Articles

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

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.

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.

Quasinormal modes and shadow of Schwarzschild Black Holes embedded in a Dehnen Type Dark Matter Halo exhibiting string cloud

Abstract In this paper, we investigate a static spherically symmetric black hole (BH) embedded in a Dehnen-(1,4,0) type dark matter (DM) halo in the presence of a cloud string. We examine and presente data on how the core density of the DM halo parameter and the cloud string parameter affect BH attributes such as quasinormal modes (QNMs) and shadow cast. To do this, we first look into the effective potential of perturbation equations for three types of perturbation fields with different spins: massless scalar field, electromagnetic field, and gravitational field. Then, using the 6th order WKB approximation, we examine quasinormal modes of the BH disturbed by the three fields and derive quasinormal frequencies. The changes of QNM versus the core density parameter and the cloud string parameter for three disturbances are explored. We also investigate how the core density and the cloud string parameters affect the photon sphere and shadow radius. Interestingly, the study shows that the influence of Dehnen type DM and cloud string increases both photon spheres and shadow radius. Finally, we employ observational data from Sgr $A{^\star}$ and $M87{^\star}$ to set limitations on the BH parameters.

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.

Photon orbits and phase transition for gravitational decoupled Kerr anti-de Sitter black holes

Interpreting the cosmological constant as the energy of the vacuum and using a gravitational decoupling approach leads to a new Kerr–anti-de Sitter (AdS) black hole. The metric of the new Kerr–AdS is more straightforward than the standard Kerr–AdS and geometrically richer, showing the rotation’s impact as a warped curvature. We investigate the relationship between the unstable photon orbits and thermodynamic phase transition to the new Kerr–AdS black hole background. We derive an exact expression for thermodynamic properties of black holes, including mass (M), Hawking temperature (T), entropy (S), heat capacity (G), and free energy (G), by relating the negative cosmological constant to positive pressure through the equation P=−Λ/8π=3/8πl2, where l represents the horizon radius, and by introducing its conjugate variable as the thermodynamic volume V. When P<Pc, black holes with CP>0 exhibit stability against thermal fluctuations, while those with CP≤0 are unstable. Our analysis of Gibbs free energy reveals a phase transition from small globally unstable black holes to large globally stable ones. Additionally, investigating the system’s P−V criticality and determining the critical exponents shows that our system shares similarities with a Van der Waals (vdW) fluid. In the reduced parameter space, we observe nonmonotonic behaviours of the photon sphere radius and the critical impact parameter when the pressure is below its critical value. It indicates that alterations in the photon sphere radius and the minimum impact parameter can act as order parameters for the phase transition between small and large black holes. In discussing the applicability of the Maxwell equal area law, we highlight the presence of a characteristic vdW-like oscillation in the P−V diagram. This oscillation, denoting the phase transition from a small black hole to a large one, can be substituted by an isobar. Furthermore, we present the distribution of critical points in parameter space and derive a fitting formula for the co-existence curve.

Survey of non-thermal electrons around supermassive black holes through polarization flips

Abstract Optically thick non-thermal synchrotron sources notably produce linear polarization vectors that are parallel to projected magnetic field lines on the observer’s screen, although they are perpendicular in well-known optically thin cases. To elucidate the complex relationship between the vectors and fields, and to investigate the energy and spatial distribution of non-thermal electrons through the images, we perform polarization radiative transfer calculations at submillimeter wavelengths. Here the calculations are based on semi-analytic force-free jet models with non-thermal electrons with a power-law energy distribution. In the calculated images, we find a $90{^\circ }$-flip of linear polarization vectors at the base of counter-side (receding) jet near a black hole, which occurs because of large optical depths for the synchrotron self-absorption effect. The $90{^\circ }$-flip of LP vectors is also seen on the photon ring at a high frequency, since the optical depth along the rays is large there due to the light bending effect. In addition, we see the flip of the sign of circular polarization components on the counter-jet and photon ring. Furthermore, we show that these polarization flips are synthesized with large values in the spectral index map, and also give rise to outstanding features in the Faraday Rotation Measure map. Since the conditions of flipping depend on the magnetic field strength and configuration and the energy distribution of electrons, we can expect that the polarization flips will provide us with observational evidence for the presence of non-thermal electrons around the black hole, and a clue to the magnetic driving mechanism of plasma jets.

Black hole horizons must be veiled by photon spheres

Black hole horizons must be veiled by photon spheres

Quasinormal modes and universality of the Penrose limit of black hole photon rings

We study the physics of photon rings in a wide range of axisymmetric black holes admitting a separable Hamilton-Jacobi equation for the geodesics. Utilizing the Killing-Yano tensor, we derive the Penrose limit of the black holes, which describes the physics near the photon ring. The obtained plane wave geometry is directly linked to the frequency matrix of the massless wave equation, as well as the instabilities and Lyapunov exponents of the null geodesics. Consequently, the Lyapunov exponents and frequencies of the photon geodesics, along with the quasinormal modes, can be all extracted from a Hamiltonian in the Penrose limit plane wave metric. Additionally, we explore potential bounds on the Lyapunov exponent, the orbital and precession frequencies, in connection with the corresponding inverted harmonic oscillators and we discuss the possibility of photon rings serving as effective holographic horizons in a holographic duality framework for astrophysical black holes. Our formalism is applicable to spacetimes encompassing various types of black holes, including stationary ones like Kerr, Kerr-Newman, as well as static black holes such as Schwarzschild, Reissner-Nordström, among others.

Improving mimetic gravity with non-trivial scalar potential: Cosmology, black holes, shadow and photon sphere

It is not easy to treat the spacetime with horizon(s) in the standard mimetic gravity. The solution to this problem has been presented in Nojiri and Nashed (2022), where it was suggested to modify the Lagrange multiplier constraint.In this paper, by using the improved formulation, we investigate the cosmology and black holes in mimetic gravity with scalar potential and in the scalar mimetic F(R) gravity. The inflationary era and dark energy epoch for the above theories are presented as specific examples from the general reconstruction scheme which permits to realize any universe expansion history via the choice of the corresponding scalar potential or function F(R). Two black hole solutions including the Schwarzschild and Hayward ones are constructed. The shadow and the radius of the photon sphere for the above black holes are found. The explicit confrontation of the black hole shadow radius with the observational bounds from M87∗ and Sgr A∗ objects is done. It is demonstrated that they do not conflict with Event Horizon Telescope observations.

Imaging fermionic dark matter cores at the centre of galaxies

ABSTRACT Current images of the supermassive black hole (SMBH) candidates at the centre of our Galaxy and M87 have opened an unprecedented era for studying strong gravity and the nature of relativistic sources. Very-long-baseline interferometry data show images consistent with a central SMBH within General Relativity (GR). However, it is essential to consider whether other well-motivated dark compact objects within GR could produce similar images. Recent studies have shown that dark matter (DM) haloes modelled as self-gravitating systems of neutral fermions can harbour very dense fermionic cores at their centres, which can mimic the space–time features of a black hole (BH). Such dense, horizonless DM cores can satisfy the observational constraints: they can be supermassive and compact and lack a hard surface. We investigate whether such cores can produce similar observational signatures to those of BHs when illuminated by an accretion disc. We compute images and spectra of the fermion cores with a general-relativistic ray tracing technique, assuming the radiation originates from standard $\alpha$ discs, which are self-consistently solved within the current DM framework. Our simulated images possess a central brightness depression surrounded by a ring-like feature, resembling what is expected in the BH scenario. For Milky Way-like haloes, the central brightness depressions have diameters down to ${\sim} 35\, \mu \text{as}$ as measured from a distance of approximately $8\,$ kpc. Finally, we show that the DM cores do not possess photon rings, a key difference from the BH paradigm, which could help discriminate between the models.

Black hole evaporation process and Tangherlini–Reissner–Nordström black holes shadow

In this article, we study the black hole evaporation process and shadow property of the Tangherlini-Reissner-Nordström (TRN) black holes. The TRN black holes are the higher-dimensional extension of the Reissner-Nordström (RN) black holes and are characterized by their mass M, charge q, and spacetime dimensions D. In higher-dimensional spacetime, the black hole evaporation occurs rapidly, causing the black hole’s horizon to shrink. We derive the rate of mass loss for the higher-dimensional charged black hole and investigate the effect of higher-dimensional spacetime on charged black hole shadow. We derive the complete geodesic equations of motion with the effect of spacetime dimensions D. We determine impact parameters by maximizing the black hole’s effective potential and estimate the critical radius of photon orbits. The photon orbits around the black hole shrink with the effect of the increasing number of spacetime dimensions. To visualize the shadows of the black hole, we derive the celestial coordinates in terms of the black hole parameters. We use the observed results of M87 and Sgr A∗ black hole from the Event Horizon Telescope and estimate the angular diameter of the charge black hole shadow in the higher-dimensional spacetime. We also estimate the energy emission rate of the black hole. Our finding shows that the angular diameter of the black hole shadow decreases with the increasing number of spacetime dimensions D.