In this paper we derive exact analytical formulas for the evolution of the photon sphere and for the angular radius of the shadow in a special Vaidya spacetime. The Vaidya metric describes a spherically symmetric object that gains or loses mass, depending on a mass function $m(v)$ that can be freely chosen. Here we consider the case that $m(v)$ is a linearly increasing or decreasing function. The first case can serve as a simple model for an accreting black hole, the second case for a (Hawking) radiating black hole. With a linear mass function the Vaidya metric admits a conformal Killing vector field which, together with the spherical symmetry, gives us enough constants of motion for analytically calculating the light-like geodesics. Both in the accreting and in the radiating case, we first calculate the light-like geodesics, the photon sphere, the angular radius of the shadow, and the red-shift of light in coordinates in which the metric is manifestly conformally static, then we analyze the photon sphere and the shadow in the original Eddington-Finkelstein-like Vaidya coordinates.
We have derived the differential equation governing the evolution of the photon sphere for dynamical black hole spacetimes with or without spherical symmetry. Numerical solution of the same depicting evolution of the photon sphere has been presented for Vaidya, Reissner-Nordström-Vaidya and de-Sitter Vaidya spacetimes. It has been pointed out that evolution of the photon sphere depends crucially on the validity of the null energy condition by the in-falling matter and may present an observational window to even test it through black hole shadow. We have also presented the evolution of the phot…
Wilczek Quantum Center, Shanghai Institute for Advanced Studies（上海高等研究院）；University of Science and Technology of China（中国科学技术大学）；Herzen state Pedagogical University of Russia（俄罗斯赫尔岑国立师范大学）；Khazar University（阿塞拜疆卡扎尔大学）；SPB branch of SAO RAS（俄罗斯科学院天体物理研究所圣彼得堡分部）；Eastern Mediterranean University（东地中海大学）
We study the analogue of the Oppenheimer-Snyder model of a collapsing sphere of homogeneous dust on the Randall-Sundrum type brane. We show that the collapsing sphere has the Vaidya radiation envelope which is followed by the brane analogue of the Schwarzschild solution described by the Reissner-Nordstrom metric. The collapsing solution is matched to the brane generalized Vaidya solution and which in turn is matched to the Reissner-Nordstrom metric. The mediation by the Vaidya radiation zone is the new feature introduced by the brane. Since the radiating mediation is essential, we are led to t…
In this paper, we study the dynamics of a hollow spherical matter collapsing with very large initial velocity. The spacetime is initially very similar to the Vaidya solution, and the deviations from this background are treated perturbatively. The equations of state for radial pressure $p_{\rm R}=kρ$ and tangential one $p_{\rm T}=wρ$ with constant $k$ and $w$ are assumed. We find for the case of equations of state $k< 1$ and $0<w\leq1$ that the initial velocity, which is nearly the speed of light, is strongly decelerated. This result implies that the pressure is essential to the property of sin…
It is generally believed that the shadows of either a black hole or naked singularity arise due to photon spheres developing in these spacetimes. Here we propose a new spherically symmetric naked singularity spacetime solution of Einstein equations which has no photon sphere, and we show that the singularity casts a shadow in the absence of the photon sphere. We discuss some novel features of this shadow and the lightlike geodesics in this spacetime. We compare the shadow of the naked singularity here with shadows cast by Schwarzschild black hole and the first type of Joshi-Malafarina-Narayan …
In this paper, we derive general conditions for a shadow to occur, without a photon sphere in a spacetime, caused by central nulllike or timelike naked singularities. Using these conditions, we propose classes of spacetimes which have nulllike and timelike naked singularities at the center, and that fulfill these `shadow without photon sphere' conditions. Considering additional asymptotically flat conditions, we show that, for a fixed Schwarzschild mass, the timelike naked singularities can cast a shadow of a size that is equal to, greater or smaller, than the size of a black hole shadow. On t…
Considering a charged black hole (BH) surrounded by a perfect fluid radiation field (PFRF) in Rastall gravity, we investigate this BH shadow and photon sphere on different spherical accretions backgrounds. The effect of the PFRF parameter/BH charge on the critical impact parameter is studied by investigating the light deflection near this BH. The luminosity of these BH shadows in different spherical accretions is obtained, respectively. It is found that the shadow of this BH with infalling spherical accretion is darker than static spherical accretion, and the photon sphere with infalling spher…
We study the shadow cast by a large gravitating sphere, similar to our Sun. For this, we consider the gravitational field produced by a static mass monopole within the first post-Newtonian approximation of the general theory of relativity. We study the propagation of a monochromatic electromagnetic wave in the vicinity of a large, opaque, gravitating sphere. To treat the opaque nature of the body and its physical size, we implement fully absorbing boundary conditions and develop a wave-optical treatment of the shadow formed by this object. Based on this approach, we demonstrate that the struct…
Analyzing the Influence of Geometrical Deformation on Photon Sphere and Shadow Radius: A New Analytical Approach -Stationary, and Axisymmetric Spacetime
In this work, we study the shadow and photon sphere of the black bole in clouds of strings and quintessence with static and infalling spherical accretions. We obtain the geodesics of the photons near a black hole with different impact parameters $b$. The string clouds model and quintessence influence the specific intensity by affecting the geodesic and the average radial position of photons. And the range of string clouds parameter $a$ is constrained to ensure that the shadow can be observed. Moreover, we use a model of the photon emissivity $j(ν_e)$ to get the specific intensities. The light …
In a recent work PRD 106, L021501 (2022), a new geometric approach is proposed to obtain the photon sphere (circular photon orbit) and the black hole shadow radius. In this approach, photon spheres and the black hole shadow radius are determined using geodesic curvature and Gaussian curvature in the optical geometry of black hole spacetimes. However, the calculations in PRD 106, L021501 (2022) only restricted to a subclass of static and spherically symmetric black holes with spacetime metric $g_{tt} \cdot g_{rr}=-1$, $g_{θθ}=r^{2}$ and $g_{ϕϕ}=r^{2}\sin^{2}θ$. In this work, we extend this appr…
For dark compact objects such as black holes or wormholes, the shadow size has long been thought to be determined by the unstable photon sphere (region). However, by considering the asymmetric thin-shell wormhole (ATSW) model, we find that the impact parameter of the null geodesics is discontinuous through the wormhole in general and hence we identify novel shadows whose sizes are dependent of the photon sphere in the other side of the spacetime. The novel shadows appear in three cases: (A2) The observer's spacetime contains a photon sphere and the mass parameter is smaller than that of the op…
It is now known that, apart from black holes, some naked singularities can also cast shadows which provide their possible observable signatures. We examine the relevant question here as to how to distinguish then these entities from each other, in terms of further physical signatures. We point out that black holes always admit timelike bound orbits having positive perihelion precession. Also, while a naked singularity with a photon sphere can cast a shadow, it could also admit positive perihelion precession for such orbits, thereby mimicking a black hole. This indicates that compact objects wi…
We consider spherically symmetric and static charged black holes in Einstein-Gauss-Bonnet-Maxwell gravities in general $D\ge 5$ dimensions and study their photon spheres and black hole shadows. We show that they all satisfy the sequence of inequalities recently proposed relating a black hole's horizon, photon sphere, shadow and its mass.
Optical appearance of regularized compact objects without an exterior photon sphere
PDPIAS, Charotar University of Science and Technology（查洛塔尔科学技术大学）；International Centre for Space and Cosmology, School of Arts and Sciences, Ahmedabad University（艾哈迈达巴德大学艺术与科学学院国际空间与宇宙学中心）
We investigate the shadows and photon spheres of the four-dimensional Gauss-Bonnet black hole with the static and infalling spherical accretions. We show that for both cases, the shadow and photon sphere are always present. The radii of the shadow and photon sphere are independent of the profiles of accretion for a fixed Gauss-Bonnet constant, implying that the shadow is a signature of the spacetime geometry and it is hardly influenced by accretion in this case. Because of the Doppler effect, the shadow of the infalling accretion is found to be darker than that of the static one. We also inves…
A photon sphere is known as the geometrical structure shaping a black hole shadow. The mechanism is well understood for static or stationary black hole spacetimes such as the Schwarzschild and the Kerr spacetimes. In this paper, we investigate and explicitly specify a photon sphere that shapes a black hole shadow in a dynamical spacetime while taking the global structure of the spacetime into account. We consider dynamical and eternal black hole cases of the Vaidya spacetime, which represents a spherically symmetric black hole with accreting null dust. First, we numerically show that there are…
Photon Spheres and Shadows of Covariant Loop Quantum Black Holes in the general $μ$-scheme
College of Physics and Electrical Engineering, Xinyang Normal University（信阳师范大学物理与电气工程学院）；School of Science, Jiangsu University of Science and Technology（江苏科技大学理学院）
We study the electromagnetic (EM) field in the shadow cast by a large opaque sphere. For this, we consider the scattering of a high frequency monochromatic EM wave by the large sphere and develop a Mie theory that accounts for the presence of this obscuration. Applying fully absorbing boundary conditions, we find a solution for the Debye potentials, which we use to determine the EM field in the shadow in the wave zone at large distances from the sphere. We use the standard tools available from the nuclear scattering theory to develop the wave-optical treatment of the problem. Based on this tre…
We review the equations determining the photon sphere radius and the black hole shadow radius, and calculate the cosmological constant corrections arising when the dark energy action has the usual form, and when dark energy arises from a Weyl scaling invariant dark energy action. For black hole targets of the Event Horizon Telescope, the corrections are very small.
In this paper, we investigate the light trajectories and shadow properties in the rotating version of null naked singularity (NNS) spacetime which is derived using the Newman- Janis algorithm without complexification method. We discuss some of the geometrical properties and causal structure of Rotating Naked Singularity (RNS) spacetime. The gravitational lensing in a rotating naked singularity is analyzed, and the results are compared to those of a Kerr black hole. In the case of a Kerr black hole, the photon sphere exists for both prograde and retrograde photon orbits, whereas for RNS, the ph…
Multimodal signatures of asymptotic (A)dS Kalb-Ramond black holes: Constraints through the shadow, weak deflection angle, and topological photon spheres
We consider a simple spherical model consisting of a Schwarzschild black hole of mass $M$ and a dark matter of mass $ΔM$ around it. The general formula for the radius of black-hole shadow has been derived in this case. It is shown that the change of the shadow is not negligible, once the effective radius of the dark matter halo is of order $\sim \sqrt{3 M ΔM}$. For this to happen, for example, for the galactic black hole, the dark matter must be concentrated near the black hole. For small deviations from the Schwarzschild limit, the dominant contribution into the size of a shadow is due to the…
We consider reflection-asymmetric thin-shell wormholes within Palatini $f(\mathcal{R})$ gravity using a matching procedure of two patches of electrovacuum space-times at a hypersurface (the shell) via suitable junction conditions. The conditions for having (linearly) stable wormholes supported by positive-energy matter sources are determined. We also identify some subsets of parameters able to locate the shell radius above the event horizon (when present) but below the photon sphere (on both sides). We illustrate with an specific example that such two photon spheres allow an observer on one of…
We wish to construct a model for charged star as a generalization of the uniform density Schwarzschild interior solution. We employ the Vaidya and Tikekar ansatz [{\it Astrophys. Astron.} {\bf 3} (1982) 325] for one of the metric potentials and electric field is chosen in such a way that when it is switched off the metric reduces to the Schwarzschild. This relates charge distribution to the Vaidya-Tikekar parameter, $k$, indicating deviation form sphericity of three dimensional space when embedded into four dimensional Euclidean space. The model is examined against all the physical conditions …
In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a $4$-dimensional black hole with a deficit solid angle and quintessence-like matter. We find that the radii of the photon sphere and shadow decrease with the decreases of the deficit solid angle and density of quintessence-like matter. The quasinormal modes are gotten by the sixth order WKB approximation method and shadow radius, respectively. The values of the real part and imaginary parts of the quasinormal modes increase with the decrease of the values of the deficit solid angle and density of quintesse…
Within 5-10 years, submillimeter VLBI facilities will be hopefully able to image the "shadow" of SgrA$^*$. When a black hole is surrounded by an optically thin emitting medium, the boundary of the shadow corresponds to the apparent photon capture sphere and only depends on the background metric. An accurate determination of the shape of the shadow of SgrA$^*$ could constrain possible deviations from the Kerr solution. In combination with other measurements, these observations could test the Kerr black hole paradigm.
Recently, an analytical solution in Einstein-aether theory was presented explicitly in isotropic coordinates. It is characterized by a mass parameter $m$ and a combined coupling constant $c_{14}$. By a coordinate transformation, we verify this solution is equivalent to the previously known static aether solution. Assuming photons couple minimally to aether and gravity, we investigate the photon sphere and shadow of the solution by varying $c_{14}$. Results are compared with those of the Schwarzschild black hole.
In this work, we study the shadow of Born-Infeld (BI) black holes with magnetic monopoles and Schwarzschild black holes immersed in the BI uniform magnetic field. Illuminated by a celestial sphere, black hole images are obtained by using the backward ray-tracing method. For magnetically charged BI black holes, we find that the shadow radius increases with the increase of nonlinear electromagnetics effects. For Schwarzschild black holes immersed in the BI uniform magnetic field, photons tend to move towards the axis of symmetric, resulting in stretched shadows along the equatorial plane.
Motivated by (i) more and more interest in strong gravitational lensing by supermassive black holes due to the achievement of EHT observations, (ii) the ongoing popular topic on the possibility of Lorentz symmetry being broken in gravitation and its consequences, we will apply the Einstein bumblebee gravity with Lorentz violation (LV) to the study of strong gravitational lensing effect and the black hole shadow of slowly rotating Kerr-like black hole. In the strong gravitational lensing sector, we first calculate the deflection angel; then treating the slowly rotating Kerr-like black hole as s…
We examine observational signatures of the asymptotically de Sitter branch of static spherically symmetric Horndeski/Galileon solutions. Our analysis reveales that possible deviations of the photon sphere size from those of the GR Schwarzshild solution are vanishing compared to the resolution of modern radio-interferometric observations. These deviations are heavily suppressed by the bounds coming from the weak-field observation. We conclude that shadow size would not be a useful characteristic to distinguish the Horndeski/Galileon static spherically symmetric spacetimes in the foreseeable fut…
Motivated by inclination of the Earth's orbit that is not located at galactic plane for observing the shadow of Sgr A*, we consider the black hole shadow for arbitrary inclinations and different velocities of observers. A surprising finding of the study is that rotation axis of a black hole might not be extracted from its shadow, since the ways of the shadow getting distorted depend not only on the spin of the black hole, but also velocities of observers. Namely, appearance of the shadow could be rotated by an angle in observers' celestial sphere due to the observer in motion. In order to furt…
In this paper, we first consider null geodesics of a class of charged, spherical and asymptotically flat hairy black holes in an Einstein-Maxwell-scalar theory with a non-minimal coupling for the scalar and electromagnetic fields. Remarkably, we show that there are two unstable circular orbits for a photon in a certain parameter regime, corresponding to two unstable photon spheres of different sizes outside the event horizon. To illustrate the optical appearance of photon spheres, we then consider a simple spherical model of optically thin accretion on the hairy black hole, and obtain the accr…
