Shadow analysis for rotating black holes in the presence of plasma for an expanding universe
Abhishek Chowdhuri, Arpan Bhattacharyya
备注：
27 pages, 6 figures, 2 tables, shadow plots and discussion regarding distortion parameter updated, references added, version to appear in Physical Review D
We explore the structure of shadow for a Kerr-de Sitter black hole with a non-magnetized, pressureless plasma surrounding it. Specific plasma distributions are considered to separate the Hamilton-Jacobi equation and find the photon regions. An analytic formula describing the boundary curve of the shadow for such a black hole in an expanding universe for an observer at any finite point outside the horizon is derived. We observe deviations which are further explored by calculating the curvature radius at a particular point for such structures in the presence and absence of plasma and calculate the diameter of the shadow.
In this paper we study the shadow of rotating Kaluza-Klein (KK) black holes and the connection between the shadow radius and the real part of quasi-normal modes (QNMs) in the eiokonal limit. In addition we have explored the quasi-periodic oscillations (QPOs) in the rotating KK black hole.
We revisit the shadow of rotating traversable wormholes discussing the role of the wormhole throat in the shadow formation. For certain classes of wormholes the throat serves as a potential barrier for light rays with particular impact parameters, thus modifying the shadow shape. We consider a couple of wormhole solutions and examine the structure of their shadow images, and the intrinsic mechanisms for their formation. Some of the shadows possess cuspy edges, which arise due to the interplay of two distinct families of unstable spherical orbits. These solutions provide examples, in which the …
We study shadows cast by a certain class of rotating wormholes and point out the crucial role of a rotating wormhole throat in the formation of a shadow. Overlooking this crucial role of a wormhole throat has resulted incomplete results in the previous studies on shadows of the same class of rotating wormholes. We explore the dependence of the shadows on the spin of the wormholes. We compare our results with that of the Kerr black hole. With increasing values of the spin, the shapes of the wormhole shadows start deviating considerably from that of the black hole. Such considerable deviation, i…
We explore the shadow of certain class of rotating traversable wormholes within classical general relativity. The images depend on the angular momentum of the wormhole, and the inclination angle of the observer. We compare the results with the case of the Kerr black hole. For small angular momenta the shadows for the two solutions are nearly identical, however with the increasing of the angular momentum they start to deviate considerably.
In this paper, we explore the photon region and the shadow of the rotating counterpart of a static charged Weyl black hole, which has been previously discussed according to null and time-like geodesics. The rotating black hole shows strong sensitivity to the electric charge and the spin parameter, and its shadow changes from being oblate to being sharp by increasing in the spin parameter. Comparing the calculated vertical angular diameter of the shadow with that of M87*, we found that the latter may possess about $10^36$ protons as its source of electric charge, if it is a rotating charged Wey…
In this paper, we construct an effective rotating loop quantum black hole (LQBH) solution, starting from the spherical symmetric LQBH by applying the Newman-Janis algorithm modified by Azreg-Aïnou's non-complexification procedure, and study the effects of loop quantum gravity { (LQG) on its shadow}. Given the rotating {LQBH}, we discuss its horizon, ergosurface, and regularity {as} $r \to 0$. Depending on the values of the specific angular momentum $a$ and the polymeric function $P$ arising from {LQG}, we {find} that the rotating solution we obtained can represent a regular black hole, a regul…
The Newman-Janis (NJ) algorithm has been extensively used in the literature to generate rotating black hole solutions from nonrotating seed spacetimes. In this work, we show, using various constants of motion, that the null geodesic equations in an arbitrary stationary and axially symmetric rotating spacetime obtained through the NJ algorithm can be separated completely, provided that the algorithm is applied successfully without any inconsistency. Using the separated null geodesic equations, we then obtain an analytic general formula for obtaining the contour of a shadow cast by a compact obj…
By exploiting the extreme environment of the black hole (BH) as a potential place for axion-photon interaction, we use an axion-producing model of the magnetized plasma to study the shadow of an asymptotically flat rotating BH immersed into an axion-plasmon cloud. By aiming to reveal footprints of axion in the dark shadow of BH, we in this paper explore the influence of the fixed axion-plasmon background on the motion of incident photons around the rotating BH. Under some free parameter settings, we find that axion-plasmon cloud around rotating BH affects the shape and size of the shadow in su…
In this work, we explore the connection between the critical curves ("shadows") and the quasinormal mode frequencies (in the eikonal limit) of Kerr black holes. This mapping has been previously established for non-rotating black holes. We show that, the shadow seen by an distant observer at a given inclination angle, can be mapped to a family of quasinormal modes with $m/(\ell+1/2)$ bounded within certain range, where $m$ is is azimuthal node number and $\ell$ is the angular node number. We discuss the possibility of testing such relation with space-borne gravitational wave detectors and the n…
We study the shadows cast by the different types of rotating regular black holes viz. Ayón-Beato-García {(ABG)}, Hayward, and Bardeen. These black holes have in addition to the total mass ($M$) and rotation parameter ($a$), different parameters as electric charge ($Q$), deviation parameter ($g$), and magnetic charge ($g_{*}$), respectively. Interestingly, the size of the shadow is affected by these parameters in addition to the rotation parameter. We found that the radius of the shadow in each case decreases monotonically and the distortion parameter increases when the value of these parameter…
A black hole casts a shadow as an optical appearance because of its strong gravitational field. We study the shadow cast by the five-dimensional Myers-Perry black hole with equal rotation parameters. We demonstrate that the null geodesic equations can be integrated that allows us to investigate the shadow cast by a black hole. The shadow of a black hole is found to be a dark zone covered by deformed circle. Interestingly, the shapes of the black hole shadow are more distorted and size decreases for larger black hole spins. Interestingly, it turns out that, for fixed values of rotation paramete…
We obtain the shadow cast induced by the rotating black hole with an anisotropic matter. A Killing tensor representing the hidden symmetry is derived explicitly. The existence of separability structure implies a complete integrability of the geodesic motion. We analyze an effective potential around the unstable circular photon orbits to show that one side of the black hole is brighter than the other side. Further, it is shown that the inclusion of the anisotropic matter ($Kr^{2(1-w)}$) has an effect on the observables of the shadow cast. The shadow observables include approximate shadow radius…
We perform the shadow calculation of the loop quantum gravity motivated regular black hole recently proposed by Ashtekar, Olmedo and Singh (will be termed AOS black hole hereafter). In the process, we also construct the rotating loop quantum gravity inspired solution of the originally proposed static spherically symmetric AOS black hole by applying the modified Newman-Janis algorithm. We study the quantum effects on the shadows of both the non-rotating and rotating loop quantum black hole solutions. It is observed that the general shape of the shadow for non-rotating AOS black hole is circular…
The shadows cast by non-rotating and rotating modified gravity (MOG) black holes are determined by the two parameters mass $M$ and angular momentum $J=Ma$. The sizes of the shadows cast by the spherically symmetric static Schwarzschild-MOG and Kerr-MOG rotating black holes increase significantly as the free parameter $α$ is increased from zero. The Event Horizon Telescope (EHT) shadow image measurements can determine whether Einstein's general relativity is correct or whether it should be modified in the presence of strong gravitational fields.
We find that the Kerr-(Newman)-AdS$_4$ black hole will be shadowless if its rotation parameter is larger than a critical value and the shadowless-ness may be related to the appearance of the null hypersurface caustics (NHC) both inside the Cauchy horizon and outside the event horizon for the black hole with the rotation parameter beyond the critical value. Our studies also further confirm that whether an ultraspinning black hole is super-entropic or not is unrelated to the existence of the NHC outside the event horizon.
The Event Horizon Telescope (EHT) observation unveiled the first image of supermassive black hole Sgr A* showing a shadow of diameter $θ_{sh}= 48.7 \pm 7\,μ$as with fractional deviation from the Schwarzschild black hole shadow diameter $δ= -0.08^{+0.09}_{-0.09}~\text{(VLTI)},-0.04^{+0.09}_{-0.10}~\text{(Keck)}$. The Sgr A* shadow size is within $~10\%$ of the Kerr predictions, providing us with another tool to investigate the nature of strong-field gravity. We use the Sgr A* shadow observables to constrain metrics of four independent and well-motivated, parametrically different from Kerr space…
We analytically investigate the influence of a cosmic expansion on the shadow of the Schwarzschild black hole. We suppose that the expansion is driven by a cosmological constant only and use the Kottler (or Schwarzschild-deSitter) spacetime as a model for a Schwarzschild black hole embedded in a deSitter universe. We calculate the angular radius of the shadow for an observer who is comoving with the cosmic expansion. It is found that the angular radius of the shadow shrinks to a non-zero finite value if the comoving observer approaches infinity.
In this paper, we construct the rotating Janis-Newman-Winicour (JNW) naked singularity spacetime using Newman-Janis Algorithm (NJA). We analyse NJA with and without complexification methods and find that the energy conditions do satisfied when we skip the complexification step. We study the shadows cast by rotating JNW naked singularity and compare them with the shadows cast by the Kerr black hole. We find that the shadow of the rotating naked singularity can be distinguished from the shadow of the Kerr black hole. While we analyse the precession of timelike bound orbits in rotating JNW spacet…
In this work, starting from a spherically symmetric scale--dependent black hole, a rotating solution is obtained by following the Newman--Janis algorithm without complexification. Besides studying the horizon, the static conditions and causality issues of the rotating solution, we get and discuss the shape of its shadow.
The existence of quintessential dark energy around a black hole has considerable consequences on its spacetime geometry. Hence, in this article, we explore its effect on horizons and the silhouette generated by a Kerr-Newman black hole in quintessential dark energy. Moreover, to analyze the deflection angle of light, we utilize the Gauss-Bonnet theorem. The obtained result demonstrates that, due to the dragging effect, the black hole spin elongates its shadow in the direction of the rotational axis, while increases the deflection angle. On the other hand, the black hole charge diminishing its …
We study the shadow of a rotating squashed Kaluza-Klein (KK) black hole and the shadow is found to possess distinct properties from those of usual rotating black holes. It is shown that the shadow for a rotating squashed KK black hole is heavily influenced by the specific angular momentum of photon from the fifth dimension. Especially, as the parameters lie in a certain special range, there is no any shadow for a black hole, which does not emerge for the usual black holes. In the case where the black hole shadow exists, the shadow shape is a perfect black disk and its radius decreases with the…
Motivated by recent work on rotating black hole shadow [Phys. Rev. D101, 084029 (2020)], we investigate the shadow behaviors of rotating Hayward-de Sitter black hole for static observers at a finite distance in terms of astronomical observables. This paper uses the newly introduced distortion parameter in [arXiv:2006.00685] to describe the shadow's shape quantitatively. We show that the spin parameter would distort shadows and the magnetic monopole charge would increase the degree of deformation. At the same time, the distortion could be relieved because of the cosmological constant and the di…
To explore the possible clues for the extra dimension from the Event Horizon Telescope (EHT) observations, we study the shadow of the rotating 5D black string in General Relativity (GR). Instead of investigating the shadow in the effective 4D theory, we concern the motion of photons along the extra dimension $z$ with a conserved momentum $P_z$, which appears as an effective mass in the geodesic equations of photons. The existence of $P_z$ enlarges the photon regions and the shadow of the rotating 5D black string while it has slight impact on the distortion. The EHT observations of M87* and Sgr…
In this paper, the shadows cast by non-rotating and rotating modified gravity black holes are investigated. In addition to the black hole spin parameter $a$ and the inclination angle $θ$ of observer, another parameter $α$ measuring the deviation of gravitational constant from the Newton one is also found to affect the shape of the black hole shadow. The result shows that, for fixed values of $a/M$ and $θ$, the size and perimeter of the shadows cast by the non-rotating and rotating black holes significantly increase with the parameter $α$, while the distortions decrease with $α$. Moreover, the …
We study the shadow of the rotating black hole with quintessential energy i) in vacuum and ii) in the presence of plasma with radial power-law density. For vacuum case the quintessential field parameter of the rotating black hole sufficiently changes the shape of the shadow. With the increasing the quintessential field parameter the radius of the shadow also increases. With the increase of the radius of the shadow of the rotating black hole the quintessential field parameter causes decrease of the distortion of the shadow shape: In the presence of the quintessential field parameter the shadow …
We have investigated the shadow of a Konoplya-Zhidenko rotating non-Kerr black hole with an extra deformation parameter. The spacetime structure arising from the deformed parameter affects sharply the black hole shadow. With the increase of the deformation parameter, the size of the shadow of black hole increase and its shape becomes more rounded for arbitrary rotation parameter. The D-shape shadow of black hole emerges only in the case $a<\frac{2\sqrt{3}}{3}M$ with the proper deformation parameter. Especially, the black hole shadow possesses a cusp shape with small eye lashes in the cases wit…
We construct a charged rotating black hole in 4D Einstein-Gauss-Bonnet (EGB) gravity starting from charged black hole in 4D EGB gravity using complex coordinate transformations suggested by Newman-Janis. Further, we have studied the null geodesics to investigate the shape of the shadow cast by a rotating charged black hole in 4D EGB gravity. Also we have discussed their horizon properties and shadow cast. The phenomenon of black hole shadows alongwith the horizon structure and energy emission has been analysed to see the influence of Gauss-Bonnet term and black hole charge on horizon, shadow, …
We study the shadow produced by a spinning Kaluza-Klein black hole in Einstein gravity coupled to a Maxwell field and a dilaton. The size and the shape of the shadow depend on the mass, the charge, and the angular momentum. We find that, for fixed values of these parameters, the shadow is slightly larger and less deformed than for its Kerr-Newman counterpart.
We investigate the horizon structure of the rotating Einstein-Born-Infeld solution which goes over to the Einstein-Maxwell's Kerr-Newman solution as the Born-Infeld parameter goes to infinity ($β\rightarrow \infty$). We find that for a given $β$, mass $M$ and charge $Q$, there exist critical spinning parameter $a_{E}$ and $r_{H}^{E}$, which corresponds to an extremal Einstein-Born-Infeld black hole with degenerate horizons, and $a_{E}$ decreases and $r_{H}^{E}$ increases with increase in the Born-Infeld parameter $β$. While $a<a_{E}$ describe a non-extremal Einstein-Born-Infeld black hole with…
The shadow of a black hole can be one of the strong observational evidences for stationary black holes. If we see shadows at the center of galaxies, we would say whether the observed compact objects are black holes. In this paper, we consider a formula for the contour of a shadow in an asymptotically-flat, stationary, and axisymmetric black hole spacetime. We show that the formula is useful for obtaining the contour of the shadow of several black holes such as the Kerr-Newman black hole and rotating regular black holes. Using the formula, we can obtain new examples of the contour of the shadow…
The recent detection of gravitational waves from black hole coalescences and the first image of the black hole shadow enhance the possibilities of testing gravitational theories in the strong-field regime. In this paper, we study the physical properties and the shadow image of a class of Kerr-like rotating black holes, whose $\mathbb{Z}_2$ symmetry is generically broken. Such black hole solutions could arise in effective low-energy theories of a fundamental quantum theory of gravity, such as string theory. Within a theory-agnostic framework, we require that the Kerr-like solutions are asymptot…
In this work, starting from a spherically symmetric polytropic black hole, a rotating solution is obtained by following the Newman--Janis algorithm without complexification. Besides studying the horizon, the static conditions and causality issues of the rotating solution, we obtain and discuss the shape of its shadow. Some other physical features as the Hawking temperature and emission rate of the rotating polytropic black hole solution are also discussed.
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…
This paper investigates the shadow of a charged rotating non-commutative black hole. For this purpose, we first formulate the null geodesics and study the effects of non-commutative charge on the photon orbit. We then explore the effect of spin, angle of inclination as well as non-commutative charge on the silhouette of the shadow. It is found that shape of the shadow deviates from the circle with the decrease in the non-commutative charge. We also discuss observable quantities to study the deformation and distortion in the shadow cast by the black hole which decreases for small values of non-…
Zhang have obtained recently a twisted rotating black hole metric, which is a vacuum solution in four-dimensional Einstein gravity. This black hole solution has a rotation parameter, but without the total angular moment. Here, we have investigated the shadow casted by a twisted rotating black hole. Our results show that the shape of the shadow of the twisted rotating black hole is a standard round disk and does not depend on the inclination angle of the observer. It means that although the twisted rotating black hole has a rotation parameter, its shadow possesses the same behaviors as the comm…
We investigate the shadow cast by a rotating braneworld black hole, in the Randall-Sundrum scenario. In addition to the angular momentum, the tidal charge term deforms the shape of the shadow. For a given value of the rotation parameter, the presence of a negative tidal charge enlarges the shadow and reduces its deformation with respect to Kerr spacetime, while for a positive charge, the opposite effect is obtained. We also analyze the case in which the combination of the rotation parameter and the tidal charge results in a naked singularity. We discuss the observational prospects correspondin…
We derived an exact solution of the spherically symmetric Hayward black hole surrounded by perfect fluid dark matter (PFDM). By applying the Newman-Janis algorithm, we generalized it to the corresponding rotating black hole. Then, we studied the shadows of rotating Hayward black hole in PFDM. The apparent shape of the shadow depends upon the black hole spin $a$, the magnetic charge $Q$ and the PFDM intensity parameter $k$ ($k<0$). The shadow is a perfect circle in the non-rotating case ($a=0$) and a deformed one in the rotating case ($a\neq{0}$). For a fixed value of $a$, the size of the shado…
We briefly review some recent advances in the study of the shadows of rotating black holes in alternative theories. The size and the shape of the shadow depend on the mass and the angular momentum, and they can also depend on other parameters specific of the particular model adopted. As an example, we show the results corresponding to a rotating braneworld black hole.
Bardeen proposed a gravitationally collapsing magnetic monopole black hole solution which is free of singularity. In this article, we have studied the size and shape of the rotating Bardeen blackhole shadow in presence of perfect fluid dark matter. we have discussed how the parameters such a spin, magnetic monopole charge and influence of dark matter affects the shadow of our blackhole. The apparent shape of the blackhole was studied by using two observables, the radius Rs and the distortion parameter R_s. Further the blackhole emission rate is also studied, we found out that for rotating Bard…
In this paper, we discuss optical properties of the topologically charged rotating black hole. We study the horizon, the photon region, the shadow of the black hole and other observables. The results show that in addition to the black hole spin parameter $a$, the other two parameters, tidal charge $β$ and electric charge $q$, are also found to affect the horizon, the photon region and the black hole shadow. In a certain range, with the increase of the three parameters, the horizon distance, shape of the photon region and the black hole shadow will all shrink. Moreover, with the increase of the…
In this paper, we study the shadow produced by rotating black holes with charge in the presence of an anisotropic matter field. We obtain the apparent shape and the corresponding observables characterizing the size, oblateness, and deviation of the center, for different values of the parameters of the model. We compare the new results with those corresponding to the Kerr-Newmann spacetime and we also discuss the observational prospects in this case.
The first image of black hole in M87 galaxy taken by Event Horizon Telescope shows that directed observation of supermassive black holes would be a promising way to test general relativity in strong gravity field regime. In order to calculate shadow of rotating black holes with respect to observers located at finite distance, orthonormal tetrads have been introduced in previous works. However, it is noticed that different choice of tetrads does not lead to the same shape of shadow for observers in near regions. In this paper, we alternatively use formula of astrometric observables for calculat…
We present an exact five-dimensional ($5D$) rotating regular black hole metric, with a deviation parameter $k\geq 0$, that interpolates between the $5D$ Kerr black hole ($k=0$) and $5D$ Kerr-Newman ($r \gg k$). This $5D$ rotating regular black hole is an exact solution of general relativity coupled to nonlinear electrodynamics. Interestingly, for a given value of parameter $k$ there exits a critical angular momentum $a=a_E$ which corresponds to extremal rotating regular black hole with degenerate horizons, while for $a<a_E$, one has non-extremal rotating regular black hole with outer and inner…
We analysed the shadow cast by charged rotating black hole (BH) in presence of perfect fluid dark matter (PFDM). We studied the null geodesic equations and obtained the shadow of the charged rotating BH to see the effects of PFDM parameter $γ$, charge $Q$ and rotation parameter $a$, and it is noticed that the size as well as the shape of BH shadow is affected due to PFDM parameter, charge and rotation parameter. Thus, it is seen that the presence of dark matter around a BH affects its spacetime. We also investigated the influence of all the parameters (PFDM parameter $γ$, BHs charge $Q$ and ro…
In this work, we study the optical properties of a class of magnetically charged rotating black hole spacetimes. The black holes in question are assumed to be immersed in the quintessence field, and subsequently, the resulting black hole shadows are expected to be modified by the presence of the dark energy. We investigate the photon region and the black hole shadow, and in particular, their dependence on the relevant physical conditions such as the state parameter of the quintessence, the angular momentum, and the magnitude of the magnetic charge. It is shown that the photon regions sensitive…
