Light Rings Research Articles

Raman scattering enhancement of dielectric microspheres on silicon nitride film

Circulating light in the total internal reflection within dielectric spheres or disks is called the whispering gallery mode (WGM), which by itself is highly sensitive to its surface and capable of detecting viruses and single atomic ions. The detection site of the sensors using WGM is created by the evanescent light from the circulating light inside spheres. Here we report anomalous Raman scattering enhancement in dielectric microspheres on a silicon nitride (SiN) film. This Raman enhancement occurs at the periphery of the spheres, and a similar ring of light was also observed under a fluorescence microscope. This is caused by the light circulating around the dielectric spheres as in the WGM. We observed anomalously enhanced Raman spectrum at the periphery of 3 μm diameter polystyrene (PS) microspheres on a SiN film using confocal laser Raman microscopy. The wavelength intensity of this enhanced Raman spectrum was accompanied by periodic changes due to interference. These features may lead to the development of high-sensitive sensors and optical devices.

Equatorial timelike circular orbits around generic ultracompact objects

For a stationary, axisymmetric, asymptotically flat, ultra-compact [$i.e.$ containing light-rings (LRs)] object, with a $\mathbb{Z}_2$ north-south symmetry fixing an equatorial plane, we establish that the structure of timelike circular orbits (TCOs) in the vicinity of the equatorial LRs, for either rotation direction, depends exclusively on the radial stability of the LRs. Thus, an unstable LR delimits a region of unstable TCOs (no TCOs) radially above (below) it; a stable LR delimits a region of stable TCOs (no TCOs) radially below (above) it. Corollaries are discussed for both horizonless ultra-compact objects and black holes. We illustrate these results with a variety of exotic stars examples and non-Kerr black holes, for which we also compute the efficiency associated with converting gravitational energy into radiation by a material particle falling under an adiabatic sequence of TCOs. For most objects studied, it is possible to obtain efficiencies larger than the maximal efficiency of Kerr black holes, $i.e.$ larger than $42\%$.

Topological Charge of Multi-Color Optical Vortices

The topological charge of an optical vortex is a quantity rather stable against phase distortions, for example, turbulence. This makes the topological charge attractive for optical communications, but for many structured beams it is unknown. Here, we derive the topological charge (TC) of a coaxial superposition of spatially coherent Laguerre–Gaussian beams with different colors, each beam with its own wavelength and its own TC. It turns out that the TC of such a superposition equals the TC of the LG beam with a longer wavelength, regardless of the weight coefficient of this beam in the superposition and regardless of its TC. It is interesting that the instantaneous TC of such a superposition is conserved on propagation, whereas the time-averaged intensity distribution of the colored optical vortex changes its gamut; if, in the near field, the colors of the light rings arrange along the radius according to their TCs in the superposition from lower to greater, then, on space propagation, the colors of the light rings in the cross-section are arranged in reverse order from the greater TC to the lower TC. We also demonstrate that, by choosing appropriate wavelengths (blue, green, and red) in a three-color superposition of single-ringed LG beams, it is possible to generate, at some propagation distance, a time-averaged light ring of the white color. If all the beams in a three-color superposition of single-ringed LG beams have the same TC, then there is a single ring of nearly white light in the initial plane. Then, on propagation in space, light rings of different colors acquire different radii: a smaller ring radius for a shorter wavelength.

Compact elastic objects in general relativity

We introduce a rigorous and general framework to study systematically self-gravitating elastic materials within general relativity, and apply it to investigate the existence and viability, including radial stability, of spherically symmetric elastic stars. We present the mass-radius ($M-R$) diagram for various families of models, showing that elasticity contributes to increase the maximum mass and the compactness up to $\approx 22\%$, thus supporting compact stars with mass well above two solar masses. Some of these elastic stars can reach compactness as high as $GM/(c^2R)\approx 0.35$ while remaining stable under radial perturbations and satisfying all energy conditions and subluminal wave propagation, thus being physically realizable models of stars with a light ring. We provide numerical evidence that radial instability occurs for central densities larger than that corresponding to the maximum mass, as in the perfect-fluid case. Elasticity may be a key ingredient to build consistent models of exotic ultracompact objects and black-hole mimickers, and can also be relevant for a more accurate modelling of the interior of neutron stars.

Sinusoidal Gaussian optical vortex as a superposition of two hypergeometric beams

We analyze the propagation of hypergeometric beams with a parabolic initial wavefront in a homogeneous medium. While hypergeomentric beams have a central amplitude singularity in the initial plane and are of infinite energy, superposition of two such beams has no singularity and is of finite energy. A particular case of such a superposition we study in detail is a sinusoidal Gaussian beam with a unit topological charge. This beam belongs to the class of elegant laser beams since it is described by the same complex-argument function both in the initial plane and in the Fresnel diffraction zone. The diameter of the first light ring of the sinusoidal Gaussian beam is almost independent of the Gaussian beam waist radius.

ECO-spotting: looking for extremely compact objects with bosonic fields

Black holes are thought to describe the geometry of massive, dark compact objects in the Universe. To further support and quantify this long-held belief requires knowledge of possible, if exotic alternatives. Here, we wish to understand how compact can self-gravitating solutions be. We discuss theories with a well-posed initial value problem, consisting in either a single self-interacting scalar, vector or both. We focus on spherically symmetric solutions, investigating the influence of self-interacting potentials into the compactness of the solutions, in particular those that allow for flat-spacetime solutions. We are able to connect such stars to hairy black hole solutions, which emerge as a zero-mass black hole. We show that such stars can have light rings, but their compactness is never parametrically close to that of black holes. The challenge of finding black hole mimickers to investigate full numerical-relativity binary setups remains open.

Light rings and long-lived modes in quasiblack hole spacetimes

It has been argued that ultracompact objects, which possess light rings but no horizons, may be unstable against gravitational perturbations. To test this conjecture, we revisit the quasi-black hole solutions, a family of horizonless spacetimes whose limit is the extremal Reissner-Nordstr\"om black hole. We find a critical parameter at which the light rings just appear. We then calculate the quasinormal modes of the quasi-black holes. Both the WKB result and the numerical result show that long-live modes survive for the range where light rings exist, indicating that horizonless spacetimes with light rings are unstable. Our work provides a strong and explicit example that light rings could be direct observational evidence for black holes.

Classification of Circular Equatorial Orbits around Regular Rotating Black Holes and Solitons with the de Sitter/ Phantom Interiors

We study the basic properties of the circular equatorial orbits for the regular axially symmetric solutions, obtained with using the Gürses–Gürsey formalism which includes the Newman–Janis algorithm, from regular spherically symmetric metrics of the Kerr–Schild class specified by Ttt=Trr. Solutions of this class describe regular rotating black holes and spinning solitons replacing naked singularities. All these objects have the interior de Sitter equatorial disk, and can have two kinds of interiors determined by the energy conditions. One of them contains an additional interior de Sitter vacuum S-surface with the de Sitter disk as a bridge, whose internal cavities are filled with a phantom fluid. We study in detail the innermost equatorial circular orbits and show that in the field of spinning solitons, the innermost orbits exist within ergoregions related to phantom regions. We show also that around spinning solitons there can exist four corotating light rings and around a regular black hole, one corotating light ring, which is stable for a certain class of black holes. For all objects there exists one counterrotating light ring.

Cuspy and fractured black hole shadows in a toy model with axisymmetry

Cuspy shadow was first reported for hairy rotating black holes, whose metrics deviate significantly from the Kerr one. The non-smooth edge of the shadow is attributed to a transition between different branches of unstable but bounded orbits, known as the fundamental photon orbits, which end up at the light rings. In searching for a minimal theoretical setup to reproduce such a salient feature, in this work, we devise a toy model with axisymmetry, a slowly rotating Kerr black hole enveloped by a thin slowly rotating dark matter shell. Despite its simplicity, we show rich structures regarding fundamental photon orbits explicitly in such a system. We observe two disconnected branches of unstable spherical photon orbits, and the jump between them gives rise to a pair of cusps in the resultant black hole shadow. Besides the cuspy shadow, we explore other intriguing phenomena when the Maxwell construction cannot be established. We find that it is possible to have an incomplete arc of Einstein rings and a “fractured” shadow. The potential astrophysical significance of the corresponding findings is addressed.

Junction conditions for generalized hybrid metric-Palatini gravity with applications

The generalized hybrid metric-Palatini gravity is a theory of gravitation that has an action composed of a Lagrangian given by $f(R,\mathcal{R})$, where $f$ is a function of the metric Ricci scalar $R$ and a new Ricci scalar $\mathcal{R}$ formed from a Palatini connection, plus a matter Lagrangian. This theory can be rewritten by trading the new geometric degrees of freedom that appear in $f(R,\mathcal{R})$ into two scalar fields, $\ensuremath{\varphi}$ and $\ensuremath{\psi}$, yielding a dynamically equivalent scalar-tensor theory. Given a spacetime theory, the next important step is to find solutions within it. To construct appropriate solutions it is often necessary to know the junction conditions between two spacetime regions at a separation hypersurface $\mathrm{\ensuremath{\Sigma}}$, with each spacetime region being an independent solution of the theory. The junction conditions for the generalized hybrid metric-Palatini gravity are found here, both in the geometric representation and in the scalar-tensor representation, and in addition, for each representation, the junction conditions for a matching with a thin-shell of matter and for a smooth matching at the separation hypersurface are worked out. These junction conditions are then applied to three configurations, namely, a star, a quasistar with a black hole, and a wormhole. The star is made of a Minkowski interior, a thin shell at the interface with all the matter energy conditions being satisfied, and a Schwarzschild exterior with mass $M$, and unlike general relativity where the matching can be performed at any radius ${r}_{\mathrm{\ensuremath{\Sigma}}}$, for this theory the matching can only be performed at a specific value of the shell radius, namely ${r}_{\mathrm{\ensuremath{\Sigma}}}=\frac{9M}{4}$, that corresponds to the general relativistic Buchdahl radius. The quasistar with a black hole is made of an interior Schwarzschild black hole surrounded by a thick shell that matches smoothly to a mass $M$ Schwarzschild exterior at the light ring radius ${r}_{\mathrm{\ensuremath{\Sigma}}e}=3M$, and with the matter energy conditions being satisfied for the whole spacetime. The wormhole is made of some interior with matter that contains the throat, a thin shell at the interface, and a Schwarzschild-AdS exterior with mass $M$ and negative cosmological constant $\mathrm{\ensuremath{\Lambda}}$, with the matter null energy condition being obeyed everywhere within the wormhole.

Light-ring pairs from A -discriminantal varieties

When geodesic equations are formulated in terms of an effective potential $\mathcal{U}$, circular orbits are characterized by $\mathcal{U}={\ensuremath{\partial}}_{a}\mathcal{U}=0$. In this paper, we consider the case where $\mathcal{U}$ is an algebraic function. Then, the condition for circular orbits defines an $A$-discriminantal variety. A theorem by Rojas and Rusek, suitably interpreted in the context of effective potentials, gives a precise criteria for certain types of spacetimes to contain at most two branches of light rings (null circular orbits), where one is stable and the other one unstable. We identify a few classes of static, spherically symmetric spacetimes for which these two branches occur.

Hale İmgesinin İnsan Dışı Varlıklarda Kullanımı ve Sanattaki Yeri Üzerine Bir Analiz

Light rings around the head or on a part of the body or surrounding the whole body used to express the holiness of figures in works of art are called “halo.” Based on artwork samples, it can be stated that the origin of the halo image is most likely Asia, dating back to 600 BC. Sometimes they are depicted as fire and sometimes they are depicted as intertwined circles. Although their usage patterns differ among cultures, similar uses are also seen due to the interaction between cultures. In Christianity, which incorporates many elements from pagan culture, aside from the icons, the holy spirit, Jesus, angels, saints, and the four Gospel writers, they are also seen on popes, saints, and the protectors of churches, the representatives of the religion. It is not common to see haloes, used as signs of holiness, on animals. However, it is seen that they are also used on some animals such as doves, eagles, bulls, lions, and lambs. Animal figures with a halo, depicted in Egyptian art, continued to have a sacred quality in Christianity. In Turkish art, the animal depictions with halo differ from those in other cultures with their secular and decorative features. In this study, first, the historical process of the halo image and its varieties in different religions, cultures, and locations will be examined, information about the haloes seen on animals will be given, which is the most important part of the subject, and an analysis will be made on its place in art.

Three-dimensional measurements of an inclined vortex ring interacting with a density stratification

Vortex rings are self-propagating structures that can transport mass and momentum to locations remote from the ring creation. We focus on the reorganization of a light vortex ring impinging, at a given angle to the vertical, a layer of fluid stably stratified in density, as in many environmental applications. We also examine the stratified layer response with regard to baroclinic vorticity and internal gravity wave generation. The symmetry of both the flow and wave field is preserved over time for normal impacts. For inclined impacts, the flow reorganizes into a vertically flattened dipolar structure and internal gravity waves radiate from two sources that match with the dipole cores.

Kerr black hole shadows in Melvin magnetic field with stable photon orbits

We have studied the spacetime of a Kerr black hole immersed in Melvin magnetic field, and found not only unstable light rings could exist, but also stable light rings could exist. Both the prograde and retrograde unstable light rings radiuses increase with the magnetic field parameter $B$, but it is the opposite for stable light rings. The existence of unstable, stable light rings depend on both the rotation parameter $a$ and the magnetic field parameter $B$. For a certain $a$, there are both the prograde and retroprade unstable (stable) light rings when $B$ is less than a critical value $B_{c}$ of retrograde light ring. In this case, the shadows of Melvin-Kerr black hole have two gray regions on both sides of the middle main shadow, which correspond to the prograde and retrograde stable photon orbits. The photons in stable orbits are always moving around Melvin-Kerr black hole, they can't enter the black hole or escape to infinity. As $B$ continues to increase, there is only the prograde unstable (stable) light ring. In this case, the gray region only emerges in the life of the main shadow, which corresponds to the prograde stable photon orbits. The absence of the retrograde unstable (stable) light rings makes the Melvin-Kerr black hole shadow an half-panoramic (equatorial) shadow. When $B$ is bigger than $B_{C}$ of prograde light ring, neither prograde nor retroprade unstable (stable) light rings exist. In this case, the shadow of Melvin-Kerr black hole has no gray region for stable photon orbits, and becomes a panoramic (equatorial) shadow. In addition, there also exist some self-similar fractal structures in the shadow of Melvin-Kerr black hole arising from the chaotic motion of photon.

Image of the thin accretion disk around compact objects in the Einstein\u2013Gauss\u2013Bonnet gravity

We study the optical appearance of a thin accretion disk around compact objects within the Einstein–Gauss–Bonnet gravity. Considering static spherically symmetric black holes and naked singularities we search for characteristic signatures which can arise in the observable images due to the modification of general relativity. While the images of the Gauss–Bonnet black holes closely resemble the Schwarzschild black hole, naked singularities possess a distinctive feature. A series of bright rings are formed in the central part of the images with observable radiation 10^3 times larger than the rest of the flux making them observationally significant. We elucidate the physical mechanism, which causes the appearance of the central rings, showing that the image is determined by the light ring structure of the spacetime. In a certain region of the parametric space the Gauss–Bonnet naked singularities possess a stable and an unstable light ring. In addition the gravitational field becomes repulsive in a certain neighbourhood of the singularity. This combination of features leads to the formation of the central rings implying that the effect is not specific for the Einstein–Gauss–Bonnet gravity but would also appear for any other compact object with the same characteristics of the photon dynamics.

Divergences in gravitational-wave emission and absorption from extreme mass ratio binaries

A powerful technique to calculate gravitational radiation from binary systems involves a perturbative expansion: if the masses of the two bodies are very different, the ``small'' body is treated as a point particle of mass ${m}_{p}$ moving in the gravitational field generated by the large mass $M$, and one keeps only linear terms in the small mass ratio ${m}_{p}/M$. This technique usually yields finite answers, which are often in good agreement with fully nonlinear numerical relativity results, even when extrapolated to nearly comparable mass ratios. Here we study two situations in which the point-particle approximation yields a divergent result: the instantaneous flux emitted by a small body as it orbits the light ring of a black hole, and the total energy absorbed by the horizon when a small body plunges into a black hole. By integrating the Teukolsky (or Zerilli/Regge-Wheeler) equations in the frequency and time domains we show that both of these quantities diverge. We find that these divergences are an artifact of the point-particle idealization, and are able to interpret and regularize this behavior by introducing a finite size for the point particle. These divergences do not play a role in black-hole imaging, e.g., by the Event Horizon Telescope.

“Spiral COSAMI” — A Multi-Undulator Compact Source for Actinic Mask Inspection in the extreme ultraviolet range

A compact electron storage ring provides a bright, stable and reliable source of extreme ultraviolet (EUV) radiation for metrology applications in semiconductor industry. The COSAMI concept (COmpact Synchrotron for Actinic Mass Inspection) applied design principles and technology of modern diffraction limited light source storage rings to an EUV facility operating at 13.5 nm wavelength. Since floor space is an important issue in an industrial environment, we propose a lattice configuration where three (or more) recirculation turns are stacked vertically. We present a facility, called Spiral-COSAMI, which simultaneously serves multiple (three or more) EUV beamlines within about the same floor space of the original COSAMI, and using the same type of injector and the same set of diagnostics, radio-frequency and pulsed magnet devices. The increased period of revolution of the multiple turns mitigates the problem of ion trapping and relaxes specifications of injection kickers.

Shadows and lensing of black holes immersed in strong magnetic fields

We investigate the null geodesic flow and in particular the light rings (LRs), fundamental photon orbits (FPOs) and shadows of a black hole (BH) immersed in a strong, uniform magnetic field, described by the Schwarzschilld-Melvin electrovacuum solution. The empty Melvin magnetic Universe contains a tube of planar LRs. Including a BH, for weak magnetic fields, the shadow becomes oblate, whereas the intrinsic horizon geometry becomes prolate. For strong magnetic fields (overcritical solutions), there are no LRs outside the BH horizon, a result explained using topological arguments. This feature, together with the light confining structure of the Melvin universe yields panoramic shadows, seen (almost) all around the equator of the observer's sky. Despite the lack of LRs, there are FPOs, including polar planar ones, which define the shadow edge. We also observe and discuss chaotic lensing, including in the empty Melvin universe, and multiple disconnected shadows.

Light rings of stationary spacetimes

We present a novel theorem regarding light rings in a stationary spacetime with an ergoregion. We prove that any stationary, axisymmetric, and asymptotically flat spacetime in 1 + 3 dimensions with an ergoregion must have at least one light ring outside the ergoregion. A possible extension of the proof for asymptotically de-Sitter and anti-de-Sitter spherically symmetric black holes is also discussed.

Shadows and optical appearance of black bounces illuminated by a thin accretion disk

We study the light rings and shadows of an uniparametric family of spherically symmetric geometries interpolating between the Schwarzschild solution, a regular black hole, and a traversable wormhole, and dubbed as black bounces, all of them sharing the same critical impact parameter. We consider the ray-tracing method in order to study the impact parameter regions corresponding to the direct, lensed, and photon ring emissions, finding a broadening of all these regions for black bounce solutions as compared to the Schwarzschild one. Using this, we determine the optical appearance of black bounces when illuminated by three standard toy models of optically and geometrically thin accretion disks viewed in face-on orientation.