Photonic Ring Research Articles

Photon Rings and Shadow Size for General Axisymmetric and Stationary Integrable Spacetimes

There are now multiple direct probes of the region near black hole horizons, including direct imaging with the Event Horizon Telescope (EHT). As a result, it is now of considerable interest to identify what aspects of the underlying spacetime are constrained by these observations. For this purpose, we present a new formulation of an existing broad class of integrable, axisymmetric, stationary spinning black hole spacetimes, specified by four free radial functions, that makes manifest which functions are responsible for setting the location and morphology of the event horizon and ergosphere. We explore the size of the black hole shadow and higher-order photon rings for polar observers, approximately appropriate for the EHT observations of M87*, finding analogous expressions to those for general spherical spacetimes. Of particular interest, we find that these are independent of the properties of the ergosphere, but do directly probe the free function that defines the event horizon. Based on those expressions, we extend the nonperturbative, nonparametric characterization of the gravitational implications of various near-horizon measurements to spinning spacetimes. Finally, we demonstrate this characterization for a handful of explicit alternative spacetimes.

The effect of scalar hair on the charged black hole with the images from accretions disk

In this paper, we investigate the optical properties of a charged black hole with scalar hair (CSH) within the context of four-dimensional Einstein–Maxwell–Dilaton gravity. To achieve this, we consider three distinct toy models of thin accretion disks. The presence of dilaton coupling allows us to express both the solutions of CSH and the Reissner–Nordström (RN) black hole in terms of their mass (M) and charge (Q). Our findings reveal differences in the effective potentials Veff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_{eff}$$\\end{document}, photon sphere radii 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}, and innermost stable circular orbit 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} between the CSH and RN black hole cases, which become increasingly pronounced as the charge parameter Q increases. However, no noticeable distinctions are observed concerning the 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}. When the ratio of the photon ring band and the lensed ring band exceeds 0.1, it may suggest the presence of a charged black hole with scalar hair. Furthermore, our results underscore the significant influence of the charge parameter Q on the brightness distributions of the direct, lensed ring, and photon ring for three standard emission functions. These findings emphasize the potential for distinguishing between CSH and RN black holes through an analysis of direct intensity and peak brightness in specific accretion disk models.

Impacts of nonthermal emission on the images of a black hole shadow and extended jets in two-temperature GRMHD simulations

The recent 230\,GHz observations from the Event Horizon Telescope (EHT) collaboration are able to image the innermost structure of the M87 galaxy showing the shadow of the black hole, a photon ring, and a ring-like structure that agrees with thermal synchrotron emission from the accretion disc. However, at lower frequencies, M87 is characterized by a large-scale jet with clear signatures of nonthermal emission. It is necessary to explore the impacts of nonthermal emission on black hole shadow images and extended jets, especially at lower frequencies. In this study, we aim to compare models with different electron heating prescriptions to one another and to investigate how these prescriptions and nonthermal electron distributions may affect black hole shadow images and the broadband spectrum energy distribution (SED) function. We performed general relativistic radiative transfer (GRRT) calculations in various two-temperature general relativistic magnetohydrodynamic (GRMHD) models utilizing different black hole spins and different electron heating prescriptions coupled with different electron distribution functions (eDFs). Through a comparison with GRRT images and SEDs, we found that when considering a variable kappa eDF, the parameterized prescription of the $R- electron temperature model with h $ = 1 is similar to the model with electron heating in the morphology of images, and the SEDs at a high frequency. This is consistent with previous studies using the thermal eDF. However, the nuance between them could be differentiated through the diffuse extended structure seen in GRRT images, especially at a lower frequency, and the behavior of SEDs at low frequency. The emission from the nearside jet region is enhanced in the case of electron heating provided by magnetic reconnection and it will increase if the contribution from the regions with stronger magnetization is included or if the magnetic energy contribution to kappa eDF mainly in the magnetized regions is considered. Compared with the thermal eDF, the peaks of the SEDs shift to a lower frequency when we consider nonthermal eDF.

Particle motion around traversable wormholes: Possibility of closed timelike geodesics

The present work investigates the general wormhole solution in Einstein gravity with an exponential shape function around an ultrastatic and a finite redshift geometry. The geodesic motion around the wormholes is studied in which the deflection angle of the orbiting photon sphere is found to be negative after a certain region, indicating the presence of repulsive effect of gravity in both the ultrastatic and finite redshift wormholes. Various unbounded and bounded timelike trajectories are presented on the wormhole embedding diagrams, in which some of the bound orbits involve intersection points that may lead to causality violating geodesics. Another class of closed timelike geodesics are obtained in the unstable circular trajectory that appeared at the wormhole throat. Finally, the trajectories are classified in terms of the family of CTG orbits.

Closed-Loop Control of Photonic Ring Resonators by Means of Photo-Thermal Plasmonic Sensors

Closed-Loop Control of Photonic Ring Resonators by Means of Photo-Thermal Plasmonic Sensors

Distinguishing the observational signatures of hot spots orbiting Reissner-Nordström spacetime*

Abstract This paper investigates observable signatures of hot spots orbiting Reissner-Nordström (RN) black holes and naked singularities. For an RN black hole, we find two discernible lensing image tracks in time integrated images, capturing a complete orbit of hot spots and a image shadow within the critical curve where photons with a small impact parameter fall into the event horizon. Conversely, in RN singularities, additional image tracks can be found within the critical curve, originating from photons reflected by the infinitely high effective potential well. Moreover, we find incomplete and converging tracks from the time integrated images of hot spot orbiting RN singularities that have no photon sphere. The presence of these additional image tracks significantly influences temporal magnitudes at their local maxima, enabling us to differentiate between RN black holes and RN naked singularities.

Testing gravitational lensing effects by supermassive massive black holes with superstring theory metric: Astrophysical implications and EHT constraints

We investigate gravitational lensing, both strong and weak, induced by charged black holes within heterotic superstring theory – α′-corrected Reissner–Nordström (RN) black holes characterized by an additional parameter, denoted as α, in addition to mass M and charge Q. Our findings reveal that as the parameter α increases, various crucial parameters such as the unstable photon orbit radius rph, critical impact parameter uph, deflection angle αD(θ), and angular position θ∞ also increase. Concurrently, the angular separation s decreases, while the relative magnitude rmag increases with the growing value of α. Utilizing supermassive black holes (SMBH) Sgr A* and M87* as gravitational lenses, the deflection angle resulting from the α′-corrected RN black hole, in both strong and weak field limits, surpasses that of the RN black holes (α=0) and falls below that of Schwarzschild black holes (α=0, Q=0). For Sgr A*, the angular position θ∞ lies within (24.08, 26.38) μas, while for M87* it ranges from (18.23, 19.96) μas. Estimating the time delay between the first and second relativistic images using twenty supermassive galactic center black holes as lenses, we find, for instance, that the time delay for Sgr A* and M87*, with Q=0.5 and α=5, can reach approximately 9.81 min and 14835.6 min, respectively. Remarkably, the EHT results for Sgr A* impose more stringent limits on the parameter space of α′-corrected RN black holes compared to those established by the EHT results for M87*. Our analysis deduces that, within the 1σ region, a substantial portion of the parameter space for α′-corrected RN black holes aligns with the Event Horizon Telescope (EHT) results for M87* and Sgr A*, and that and one cannot rule out the possibility of that heterotic superstring theory’s α′-corrected RN black holes being strong candidates for astrophysical black holes.

General upper limit on the electric charge of Sgr A* in the Reissner–Nordström metric

ABSTRACT In general relativity, the gravitational field of an electrically charged, non-rotating, spherically symmetric body is described by the Reissner–Nordström (RN) metric. Depending on the charge to mass ratio, the solution describes a black hole or a naked singularity. In the naked-singularity regime, a general property of this metric is the existence of a radius, known as the zero-gravity radius, where a test particle would remain at rest. As a consequence of repulsive gravity there is no circular orbit inside this radius, and at least a part of any quasi-stable structure must necessarily lie outside of it. Assuming the iconic torus in the compact source Sgr A* at the Galactic centre observed by the Event Horizon Telescope (EHT) to be the image of a quasi-stationary fluid structure, we provide rigorous constraints in the RN metric on the electric charge-to-mass ratio Q/M of Sgr A*. A comparison between the EHT observations and the space–time zero-gravity radius provides the most conservative limit on the charge of Sgr A* to be |Q/M| < 2.32 in geometrized units. A charged naked singularity respecting this charge-to-mass constraint is consistent with the current EHT observations, if the image is not interpreted as a photon ring.

Shadow of novel rotating black hole in GR coupled to nonlinear electrodynamics and constraints from EHT results

We study the optical properties of spacetime around a novel black hole in general relativity coupled to nonlinear electrodynamics, which is asymptotically flat. First, we study the angular velocity and Lyapunov exponent in unstable photon circular orbits in the novel spherically symmetric black hole spacetime. Later, we obtain the rotating black hole solution using the Newman–Janis algorithm and determine the event horizon properties of the black hole. We analyze the effective potential for the circular motion of photons in the spacetime of the novel rotating black hole. Also, we analyze the photon sphere around the novel black hole and its shadow using celestial coordinates. We obtain that an increase of the black hole spin and charge as well as nonlinear electrodynamics field nonlinearity parameters causes an increase in the distortion parameter of the black hole shadow, while, the area of the shadow and its oblateness decrease. Moreover, we also obtain the constraint values for the black hole charge and the nonlinearity parameters using Event Horizon Telescope data from shadow sizes of supermassive black holes Sgr A* and M87*. Finally, the emission rate of black hole evaporation through Hawking radiation is also studied.

Black hole solutions with constant Ricci scalar in a model of Finsler gravity

Ricci scalar being zero is equivalent to the vacuum field equation in Finsler space-time. The Schwarzschild metric can be concluded from the field equation's solution if the space-time conserves spherical symmetry. This research aims to investigate Finslerian Schwarzschild-de Sitter space-time. Recent studies based on Finslerian space-time geometric models are becoming more prevalent because the local anisotropic structure of space-time influences the gravitational field and gives rise to modified cosmological relations. We suggest a gravitational field equation with a non-zero cosmological constant in Finslerian geometry and apprehend that the presented Finslerian gravitational field equation corresponds to the non-zero Ricci scalar. In Finsler geometry, the peer of spherical symmetry is the Finslerian sphere. Assuming space-time to conserve the “Finslerian sphere” symmetry, the counterpart of the Riemannian sphere (Finslerian sphere) must have a constant flag curvature (λ). It is demonstrated that the Finslerian covariant derivative of the geometric part of the gravitational field equation is preserved under a condition using the Chern connection. According to the string theory, string clouds can be defined as a pool of strings made due to symmetry breaking in the universe's early stages. We find that for λ ≠ 1, this solution resembles a black hole surrounded by a cloud of strings. Furthermore, we investigate null and time-like geodesics for λ = 1. In this regard, the photon geodesics are obtained that are the closest paths to the photon sphere of the first photons visible at the black hole shadow limit. Also, circular orbit conditions are obtained for the effective potential.

Gaussian black holes in brane-world model

We present regular black hole solutions in the framework of Brane-world gravity sourced by a Gaussian matter distribution. The black hole metric shares all the common features of regular black holes in the modified General Relativity (GR) with some exciting features. Considering the energy momentum tensor for an isotropic fluid on the brane, the modified Einstein field equation results with an effective energy momentum tensor that describes an anisotropic fluid determined by brane world parameters. Although the effective radial pressure and energy density satisfy the vacuum energy condition, the effective transverse pressure behaves differently. Gaussian black hole (GBH) solutions are obtained from a Gaussian matter distribution. In the paper, a new class of GBH solutions are obtained in the brane-world gravity with effective normal matter in addition to exotic matter distribution. In the brane world gravity, the mass of a GBH depends on the brane tension. The mass of a GBH formed in the brane world is greater than that at low energy (i.e., GR). We study the trajectories of the massive and the massless particles that can be trapped around a GBH for a set of model parameters. The radii of the photon spheres around the GBH and the condition for the stability of the trajectories of the photon spheres are determined. The properties of the GBHs are studied in detail, including their possible observable features.

Photon orbits and phase transition for Letelier AdS black holes immersed in perfect fluid dark matter

Abstract We obtain an exact solution of spherically symmetric Letelier AdS black holes immersed in perfect fluid dark matter (PFDM). Considering the cosmological constant as the positive pressure of the system and volume as its conjugate variable, we analyse the thermodynamics of our black holes in the extended phase space. Owing to the background clouds of strings parameter ($a$) and the parameter endowed with PFDM ($\beta$), we analyse the Hawking temperature, entropy and specific heat. We also investigate the relationship between the photon sphere radius and the phase transition for the Letelier AdS black holes immersed in PFDM. Through the analysis, we find with a particular condition, there are non-monotonic behaviours between the photon sphere radius, the impact parameter, the PFDM parameter, temperature, and pressure. We can regard both the changes of photon sphere radius and impact parameter before and after phase transition as the order parameter; their critical exponents near the critical point are equal to the same value 1/2, just like ordinary thermal systems. These indicate that a universal relation of gravity may exist near the critical point for a black hole thermodynamic system.

Light propagation in a plasma on Kerr spacetime. II. Plasma imprint on photon orbits

Light propagation in a plasma on Kerr spacetime. II. Plasma imprint on photon orbits

Holographic image features of Hayward-AdS black hole surrounded by quintessence dark energy

By employing the AdS/CFT correspondence, we investigate the holographic images of Hayward-AdS black hole enveloped by quintessence dark energy. The AdS boundary is equipped with a Gaussian oscillation source, which give rise to the response generated on the opposing side of the boundary after it propagated in the bulk. With the aid of a special wave optics system, the holographic images of black hole in the bulk can be constructed. When the observation position is located at the north pole of boundary, the virtual screen displays a sequence of closed concentric ring structures. There is invariably one of these rings consistently marked by an exceptionally high level of observational intensity, namely the holographic Einstein ring, which corresponds to the position of photon ring in the geometric optics. For other observation positions, the ring transforms gradually into a luminous arc-like shape and ultimately into a light spot positioned on the screen. And, the effects of the relevant state parameters on the characteristics of black hole holographic image, including the observed intensity, width or size of the ring, and proportion range, are in-depth examined. It is believed that the critical information of the Hayward-AdS black hole surrounded by quintessence can be obtained from these holographic images, which will help us understand the geometric characteristics of regular spacetime more deeply.

Ultrasensitive Silicon Photonic Refractive Index Sensor Based on Hybrid Double Slot Subwavelength Grating Microring Resonator.

Silicon photonic-based refractive index sensors are of great value in the detection of gases, biological and chemical substances. Among them, microring resonators are the most promising due to their compact size and narrow Lorentzian-shaped spectrum. The electric field in a subwavelength grating waveguide (SWG) is essentially confined in the low-refractive index dielectric, favoring enhanced analyte-photon interactions, which represents higher sensitivity. However, it is very challenging to further significantly improve the sensitivity of SWG ring resonator refractive index sensors. Here, a hybrid waveguide blocks double slot subwavelength grating microring resonator (HDSSWG-MRR) refractive index sensor operating in a water refractive index environment is proposed. By designing a new waveguide structure, a sensitivity of up to 1005 nm/RIU has been achieved, which is 182 nm/RIU higher than the currently highest sensitivity silicon photonic micro ring refractive index sensor. Meanwhile, utilizing a unique waveguide structure, a Q of 22,429 was achieved and a low limit of detection of 6.86 × 10-5 RIU was calculated.

Observational appearance and extra photon rings of an asymmetric thin-shell wormhole with a Bardeen profile* *Supported by the National Natural Science Foundation of China (11903025), the Science and Technology Program of Sichuan Province, China(2023ZYD0023), and the starting fund of China West Normal University (18Q062)

In this work, the optical appearance of an asymmetric thin-shell wormhole with a Bardeen profile is studied. To initiate the process, we need to construct an asymmetric thin-shell wormhole utilizing the cut-and-paste technique proposed by Visser and subsequently ascertain its pertinent physical quantities such as the radius of the photon sphere and critical impact parameters for different values of magnetic charge g. Then, the effective potential and motion behavior of photons are also investigated within the framework of asymmetric thin-shell wormholes with a Bardeen profile. It can be found that the effective potential, ray trajectory, and azimuthal angle of the thin-shell wormhole exhibit a strong correlation with the mass ratio of black holes. By considering the accretion disk as the sole background light source, we observe additional photon rings and lensing bands in the optical appearance of the asymmetric thin-shell wormhole with a Bardeen profile compared to those exhibited by the Bardeen black hole. One can find that there is an increase in the size of the specific additional light bands with increasing magnetic charge g, which is different from the black hole case. These exceptionally luminous rings can serve as a robust criterion for the identification and characterization of the thin-shell wormhole spacetime.

Observations of orbiting hot spots around scalarized Reissner–Nordström black holes

This paper investigates the observational signatures of hot spots orbiting scalarized Reissner–Nordström black holes, which have been reported to possess multiple photon spheres. In contrast to the single-photon sphere case, hot spots orbiting black holes with two photon spheres produce additional image tracks in time integrated images capturing a complete orbit of hot spots. Notably, these newly observed patterns manifest as a distinct second-highest peak in temporal magnitudes when observed at low inclination angles. These findings offer promising observational probes for distinguishing black holes with multiple photon spheres from their single-photon sphere counterparts.

Photon ring autocorrelations from gravitational fluctuations around a black hole

Photon ring autocorrelations from gravitational fluctuations around a black hole

Accelerating AdS black holes in gravity’s rainbow

Motivated by the effect of the energy of moving particles in C-metric, we first obtain exact accelerating black hole solutions in gravity’s rainbow. Then, we study the effects of gravity’s rainbow and C-metric parameters on the Ricci and Kretschmann scalars, and also the asymptotical behavior of this solution. Next, we indicate how different parameters of the obtained accelerating black holes in gravity’s rainbow affect thermodynamics quantities (such as the Hawking temperature, and entropy) and the local stability (by evaluating the heat capacity). In the following, we extract the geodesic equations to determine the effects of various parameters on photon trajectory in the vicinity of this black hole, as well as obtain the radius of the photon sphere and the corresponding critical impact parameter to gain insight into AdS black hole physics by adding the gravity’s rainbow to C-metric.

Shadows and photon rings of a quantum black hole

Recently, a black hole model in loop quantum gravity has been proposed by Lewandowski, Ma, Yang and Zhang (2023) [34]. The metric tensor of the quantum black hole (QBH) is a suitably modified Schwarzschild one. In this paper, we calculate the radius of the circular null geodesic (light ring) and obtain the linear approximation of it with respect to the quantum correction parameter α: rl≃3M−α9M. We then assume the QBH is backlit by a large, distant plane of uniform, isotropic emission and calculate the radius of the black hole shadow and its linear approximation: rs=33M−α6(3M). We also consider the photon ring structures in the shadow when the impact parameter b of the photon approaches to a critical impact parameter bc, and obtain a formula for estimating the deflection angle, which is φdef=−2ωrl2log⁡(1−bc/b)+C˜(bc). We also numerically plot the images of shadows and photon rings of the QBH in three different illumination models and compare them with that of a Schwarzschild black hole. It is found that we could distinguish the quantum black hole with a Schwarzschild black hole via the shadow images in certain illumination models.