We present firstly the equation of motion for the photon coupled to a special bumblebee vector field in a Kerr black hole spacetime and find that the propagation of light depends on its polarization due to the birefringence phenomenon. The dependence of black hole shadow on the light's polarization is dominated by the rotation of black hole. In the non-rotating case, we find that the black hole shadow is independent of the polarization of light. However, the status is changed in the rotating case, in which the black hole shadow depends on the light's polarization and the coupling between bumblebee vector field and electromagnetic field. These features of black hole shadow casted by polarized lights could help us to understand the bumblebee vector field with Lorentz symmetry breaking and its interaction with electromagnetic field.
It is shown that the paper "Greybody radiation and quasinormal modes of Kerr-like black hole in Bumblebee gravity model", Eur. Phys. J. C 81, 501 (2021). arXiv:2102.06303, recently published in this journal is based on an incorrect result obtained by Ding et al., Eur. Phys. J. C 80, 178 (2020). arXiv:1910.02674, for a Kerr-like black hole solution.
Constrain from shadows of $M87^*$ and $Sgr A^*$ and quasiperiodic oscillations of galactic microquasars on a black hole arising from metric-affine bumblebee model
In this paper, we study the weak gravitational deflection angle of relativistic massive particles by the Kerr-like black hole in the bumblebee gravity model. In particular, we focus on weak field limits and calculate the deflection angle for a receiver and source at a finite distance from the lens. To this end, we use the Gauss-Bonnet theorem of a two-dimensional surface defined by a generalized Jacobi metric. The spacetime is asymptotically non-flat due to the existence of a bumblebee vector field. Thus the deflection angle is modified and can be divided into three parts: the surface integral…
Lorentz-Violating (LV) scenario gets involved through a bumblebee field vector field $B_μ$. A spontaneous symmetry breaking allows the field to acquires a vacuum expectation value that generates LV into the system. A Kerr-Sen-like solution has been found out starting from the generalized form of a radiating stationery axially symmetric black-hole metric. We compute the effective potential offered by the null geodesics in the bumblebee rotating black-hole spacetime. The shadow has been sketched for different variations of the parameters involved in the system. A careful investigation has been c…
In the Einstein-bumblebee gravity, the Lorentz symmetry is spontaneously broken by a vector field. In this paper, we attempt to test the Lorentz symmetry via the observation of the shadow cast by the Kerr-like black hole with or without plasma. A novel phenomenon of the Lorentz-violating parameter on the shadow is observed. The result shows that when the observer gradually moves from the poles to the equatorial plane, the shadow radius $R_{\rm s}$ firstly decreases and then increases with the Lorentz-violating parameter. Such nonmonotonic behavior provides us an important understanding on the …
We study the accretion process in the thin disk around a rotating Kerr-like black hole in Einstein-bumblebee gravity model where Lorentz symmetry is spontaneously broken once a vector field acquires a vacuum expectation value. In the present paper we obtain the energy flux, the emission spectrum and accretion efficiency from the accretion disks around the rotating Kerr-like black hole, and we compare them to the general Kerr case. These significant features in the mass accretion process may provide a possibility to test whether the Lorentz symmetry is spontaneously broken or not in the Einstei…
In the framework of the Lorentz symmetry breaking (LSB), we investigate the quasinormal modes (QNMs) and the greybody factors (GFs) of the Kerr-like black hole spacetime obtained from the bumblebee gravity model. In particular, we analyze the scalar and fermionic perturbations of the black hole within the framework of both semi-analytic WKB method and the time domain approach. The impacts of the LSB on the bosonic/fermionic QNMs and GFs of the Kerr-like black hole are investigated in detail. The obtained results are graphically depicted and discussed.
Imprints of Black Hole Shadows and Polarization Patterns of Various Thick Disks: Bumblebee gravity
University of Management and Technology（管理技术大学）；Princess Nourah bint Abdulrahman University（公主努拉·宾特·阿卜杜勒·拉赫曼大学）；Chongqing Jiaotong University（重庆交通大学）；Chongqing Normal University（重庆师范大学）
In our recent study Ref. [1]: Eur. Phys. J. C 81, 501 (2021) , the main goal was to reveal the Lorentz symmetry breaking (LSB) effect in the rotating black holes via the greybody factor and quasinormal mode analyzes. Ding et al. [2] Kerr-like black hole solution of the bumblebee gravity model used in our paper [1] has unquestionably proven by Maluf and Muniz [3] that it is wrong. We now explain under which condition the greybody factor and quasinormal mode analyzes performed in [1] become valid. We re-make the calculations according to the condition in question and present the new results in t…
Rotating Black Holes and the Kerr/CFT Correspondence in Einstein-Bumblebee Gravity
Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）；School of Physics and Electronics, Hunan University（湖南大学物理与电子学院）
In this paper, we derive an exact black hole spacetime metric in the Einstein-Hilbert-Bumblebee (EHB) gravity around global monopole field. We study the horizon, temperature, and the photon sphere of the black hole. Using the null geodesics equation, we obtain the shadow cast by the Schwarzschild-like black hole with a topological defect in bumblebee gravity. Interestingly, the radius of shadow of the black hole increases with increase in the global monopole parameter. We also visualize the shadows and energy emission rates for different values of parameters. Moreover, using the Gauss-Bonnet t…
In this work, we present black hole solutions with a cosmological constant in bumblebee gravity, which provides a mechanism for the Lorentz symmetry violation by assuming a nonzero vacuum expectation value for the bumblebee field. From the gravitational point of view, such solutions are spherically symmetric black holes with an effective cosmological constant and are supported by an anisotropic energy-momentum tensor, conceived of as the manifestation of the bumblebee field in the spacetime geometry. Then we calculate the shadow angular radius for the proposed black hole solution with a positi…
A Kerr-Sen-like black hole solution appears in the Einstein-bumblebee theory of gravity. The solution contains contains a Lorentz violating parameter in an explicit manner. We study the null geodesics in the background of this Kerr-Sen-like black hole surrounded by a dispersive medium like plasma. We investigate the effect of the charge of the black hole, the Lorentz violation parameter, and the plasma parameter on the photon orbits with the evaluation of the effective potential in the presence of both the Lorentz violation parameter and the plasma parameter. We also study the influence of the…
Weak field deflection angle and analytical parameter estimation of the Lorentz-violating Bumblebee parameter through the black hole shadow using EHT data
After recent observational events like the LIGO-Virgo detections of gravitational waves and the shadow image of M87* supermassive black hole by Event Horizon Telescope (EHT), the theoretical study of black holes was significantly improved. Quantities as quasinormal frequencies, shadows, and light deflection become more important to analyze black hole models. In this context, an interesting scenario to study is a black hole in the bumblebee gravity. The bumblebee vector field imposes a spontaneous symmetry breaking that allows the field to acquire a vacuum expectation value that generates Loren…
The first images of black hole shadows open new possibilities to constrain modern extended gravity theories. We present the method of shadow background calculation for black hole solutions in the form of Taylor series where $g_{11} = - g_{00}^{-1}$. The method is extended to general non-rotating case $g_{11} \neq - g_{00}^{-1}$. The results of the analysis are compared with the predictions of General relativity taking into account the Event Horizon Telescope data. The results for the Horndesky model with the Gauss-Bonnet invariant, loop quantum gravity, Bumblebee model and Gauss-Bonnet gravity…
East China University of Science and Technology（华东理工大学）；Universidade Federal da Paraíba（帕拉伊巴联邦大学）；Universidade Federal de Campina Grande（坎皮纳大联邦大学）；Khazar University（哈扎尔大学）
An exact Kerr-like solution has been obtained recently in Einstein-bumblebee gravity model where Lorentz symmetry is spontaneously broken. In this paper, we investigate the superradiant instability of the Kerr-like black hole under the perturbation of a massive scalar field. We find the Lorentz breaking parameter $L$ does not affect the superradiance regime or the regime of the bound states. However, since $L$ appears in the metric and its effect cannot be erased by redefining the rotation parameter $\tilde{a}=\sqrt{1+L}a$, it indeed affects the bound state spectrum and the superradiance. We c…
This work belongs to the context of the standard-model extension, in which a Lorentz symmetry violation is induced by a bumblebee field as it acquires a nonzero vacuum expectation value. The mathematical formulation of a generic bumblebee model and its associated dynamical equations are presented. Then, these equations are considered for the vacuum and a substantial simplification is performed for the particular case of a gradient bumblebee field at its vacuum expectation value. After some further manipulation, a method to easily find solutions to the model is developed, in which the exact eff…
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 report the existence of novel static spherical black-hole solutions in a vector-tensor gravitational theory called the bumblebee gravity model which extends the Einstein-Maxwell theory by allowing the vector to nonminimally couple to the Ricci curvature tensor. A test of the solutions in the strong-field regime is performed for the first time using the recent observations of the supermassive black-hole shadows in the galaxy M87 and the Milky Way from the Event Horizon Telescope Collaboration. The parameter space is found largely unexcluded and more experiments are needed to fully bound the …
A Kerr-Sen-like black hole solution results from Einstein-bumblebee gravity. It contains a Lorentz violating (LV) parameter that enters when the bumblebee field receives vacuum expectation value through a spontaneously breaking of the symmetry of the classical action. The geometrical structure concerning the singularity of this spacetime is studied with reference to the parameters involved in the Kerr-Sen-like metric. We introduce this Einstein-bumblebee modified gravity to probe the role of spontaneous Lorentz violation on the superradiance scattering phenomena and the instability associated …
The correspondence between the shadow radius and the quasi-normal modes of the Kerr-Sen black hole is studied. By using the equation of the shadow radius of the Kerr-Sen black hole and the angular separation constant of the quasi-normal modes, the expression of the real part of quasi-normal modes related to the shadow radius is obtained. We found that in the eikonal limit, our formula coincides with the previous result. Moreover, we also calculate the energy emission rate of the Kerr-Sen black hole, it turns out that the peak energy emissivity is inversely correlated with the charge parameter.
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.
Investigations of shadows of astrophysical entities constitute a major source of insight into the evolution of compact objects. Such effects depend on the nature of the compact object and arise on account of the strong gravitational lensing that casts a shadow on the bright background. We consider the Kerr-like wormhole spacetime (Phys.\ Rev.\ D 97:024040, 2018), which is a modification of the Kerr black hole that degenerates into wormholes for nonzero values of the deviation parameter $λ^2$. The results suggest that the Kerr spacetime can reproduce far away from the throat of the wormhole. We…
Thermodynamics and Optical Properties of Charged Black Holes in Bumblebee gravity Sourced by a Cloud of Strings
The Assam Royal Global University（阿萨姆皇家全球大学）；The Institute of Mathematical Sciences, C. I. T. Campus（马哈拉施特拉理工学院数学科学研究所）；Al-Hussein Bin Talal University（侯赛因·本·塔拉勒大学）
We explore the shadow of certain class generalized Kerr black holes, which are non vacuum solutions of the Einstein equations with exotic matter. The images depend on the angular momentum of the compact object, the characteristic parameter $l$ of the model, and the inclination angle of the observer. The results are compared with the case of the Kerr black hole and the Kerr naked singularity.
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 have studied the shadow of a disformal Kerr black hole with an extra deformation parameter, which belongs to non-stealth rotating solutions in quadratic Degenerate Higher Order Scalar Tensor (DHOST) theory. Our result show that the size of the shadow increases with the deformation parameter for the black hole with arbitrary spin parameter. However, the effect of the deformation parameter on the shadow shape depends heavily on the spin parameter of black hole and the sign of the deformation parameter. The change of the shadow shape becomes more distinct for the black hole with the more quick…
We analyze the shadow of charged stationary axially symmetric space-time (Kerr-Sen dilaton-axion black hole). This black hole is defined by a mass $M$, a spin $a$ and $r_α=Q^{2}/M$, where $Q$ is the electric charge. Shadows are investigated in two conditions, i) for an observer at infinity in vacuum and ii) for an observer at infinity in the presence of plasma with radial power-low density. In vacuum, the shadow of this black hole depends on charge and spin parameter. We can see that, increasing electric charge, $Q$ decreases the size of shadow. Also, increasing spin parameter $a$ decreases th…
The Event Horizon Telescope collaboration has revealed the first direct image of a black hole, as per the shadow of a Kerr black hole of general relativity. However, other Kerr-like rotating black holes of modified gravity theories cannot be ignored, and they are essential as they offer an arena in which these theories can be tested through astrophysical observation. This motivates us to investigate asymptotically de Sitter rotating black holes wherein interpreting the cosmological constant $Λ$ as the vacuum energy leads to a deformation in the vicinity of a black hole -- new Kerr--de Sitter s…
We study the shadow cast or silhouette generated by a Kerr-Newman-Kasuya (KNK) spacetime (rotating dyon black hole). It is shown that in addition to the angular momentum of the black hole, the dyon charge also affects the shadow image of the KNK black hole. Moreover, we analyze the weak gravitational lensing by the KNK black hole by using the Gauss-Bonnet theorem. Finally, we find that extra dyon charge decreases both the deflection angle and shadow of the KNK black hole.
It is now known that the shadow is not only the property of a black hole, it can also be cast by other compact objects like naked singularities. However, there exist some novel features of the shadow of the naked singularities which are elaborately discussed in some recent articles. In the earlier literature, it is also shown that a naked singularity may admit negative precession of bound timelike orbits which cannot be seen in Schwarzschild and Kerr black hole spacetimes. This distinguishable behavior of timelike bound orbit in the presence of the naked singularity along with the novel featur…
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…
This work is geared towards analysis of shadows cast by Kerr-de Sitter (KdS) and Kerr-de Sitter Revisited (RKdS) black holes. Considering observers in the vicinity of the static radius, we derive the impact parameters defining the apparent positions of the shadows. Such observers are of interest to our work because embedding diagrams have shown that de Sitter space-time is analogous to an asymptotically flat one in the vicinity of the static radius. We also perform a comparative analysis between our result with that in Ref.[1]. Furthermore, we numerically obtain the radii of curvature, vertica…
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…
In this paper we have took reissner nordstrom blackhole with cloud of strings and surrounds it with quintessence. we processed the metric through newman janis algorithm to get its rotating counterpart. the blackhole in study now is a roating charged blackhole with clouds of string surrounded by quintessence. we studied its nature of effective potential and unstable photon orbits. Finally we have plotted the blackhole shadow for various variable profiles.
