Shadows and amplitude luminosity of an embedded rotating black hole

A mathematically consistent rotating black hole model in loop quantum gravity (LQG) is yet lacking. The scarcity of rotating black hole solutions in LQG substantially hampers the development of testing LQG from observations, e.g., from the Event Horizon Telescope (EHT) observations. The EHT observation revealed event horizon-scale images of the supermassive black holes Sgr A* and M87*. The EHT results are consistent with the shadow of a Kerr black hole of general relativity. We present LQG-motivated rotating black hole (LMRBH) spacetimes, which are regular everywhere and asymptotically encompass the Kerr black hole as a particular case. The LMRBH metric describes a multi-horizon black hole in the sense that it can admit up to three horizons, such that an extremal LMRBH, unlike the Kerr black hole, refers to a black hole with angular momentum a > M. The metric, depending on the parameters, describes (1) black holes with only one horizon (BH-I), (2) black holes with an event horizon and a Cauchy horizon (BH-II), (3) black holes with three horizons (BH-III), or (4) no-horizon spacetime, which we show is almost ruled out by EHT observations. We constrain the LQG parameter with the aid of the EHT shadow observational results of M87* and Sgr A*, respectively, for inclination angles of 17° and 50°. In particular, the VLTI bound for Sgr A*, δ ∈ (−0.17, 0.01), constrains the parameters (a, l) such that for 0 < l ≤ 0.347851M (l ≤ 2 × 106 km), the allowed range of a is (0, 1.0307M). Together with the EHT bounds of Sgr A* and M87* observables, our analysis concludes that a substantial part of BH-I and BH-II parameter space agrees with the EHT results of M87* and Sgr A*. While the EHT M87* results totally rule out BH-III, but not that by Sgr A*.

The Event Horizon Telescope (EHT) recently released an image of the supermassive black hole Sgr A* showing an angular shadow diameter d sh = 48.7 ± 7 μas and Schwarzschild shadow deviation , using a black hole mass . The EHT image of Sgr A* is consistent with a Kerr black hole’s expected appearance, and the results directly prove the existence of a supermassive black hole at the center of the Milky Way. Here, we use the EHT observational results for Sgr A* to investigate the constraints on its charge with the aid of Kerr-like black holes, paying attention to three leading rotating models, namely Kerr–Newman, Horndeski, and hairy black holes. Modeling the supermassive black hole Sgr A* as these Kerr-like black holes, we observe that the EHT results for Sgr A* place stricter upper limits on the parameter space of Kerr–Newman and Horndeski black holes than those placed by the EHT results for M87*. A systematic bias analysis reveals that observational results from future EHT experiments will place more precise limits on the charge of the black hole Sgr A*. Thus, the Kerr-like black holes and Kerr black holes are indiscernible in a substantial region of the EHT-constrained parameter space; the claim is substantiated by our bias analysis.

In this work, we mainly focus on testing the spacetime properties around black holes surrounded by a dark fluid, which are potential candidates for dark energy described by the Chaplygin-like equation of state through its shadow. To do this, we first study the black hole’s horizon structure and shadow for the non-rotating case. Then, we obtain a rotating black hole solution in the presence of a dark fluid using the generalized Newman–Janis algorithm and study the effects of the black hole spin and the fluid parameters on the black hole horizons. Also, we obtained the shadow cast of the rotating black hole using celestial coordinates and showed that the presence of the dark fluid causes an increase in shadow size. Moreover, we use the shadow size of supermassive black holes Sagittarius A* and M87* from Event Horizon Telescope observations to obtain constraints on the spin, black hole charge, and dark fluid parameters. Lastly, we investigate the energy emission rate of a charged black hole surrounded by a Chaplygin-like dark fluid, comparing it to both rotating and non-rotating cases.

We present the first observational evidence that light propagating near a rotating black hole is twisted in phase and carries orbital angular momentum (OAM). This physical observable allows a direct measurement of the rotation of the black hole. We extracted the OAM spectra from the radio intensity data collected by the Event Horizon Telescope from around the black hole M87* by using wavefront reconstruction and phase recovery techniques and from the visibility amplitude and phase maps. This method is robust and complementary to black hole shadow circularity analyses. It shows that the M87* rotates clockwise with an estimated rotation parameter a = 0.90 ± 0.05 with an $\sim 95{{\ \rm per\ cent}}$ confidence level (c.l.) and an inclination i = 17° ± 2°, equivalent to a magnetic arrested disc with an inclination i = 163° ± 2°. From our analysis, we conclude that, within a 6σ c.l., the M87* is rotating.

Exploring perfect fluid dark matter with EHT results of Sgr A* through rotating 4D-EGB black holes

We consider a timelike geodesics in the background of rotating Einstein-Born-Infeld (EBI) black hole to examine the horizon and ergosphere structure. The effective potential that governs the particle's motion in the spacetime and the innermost stable circular orbits (ISCO) is also studied. A qualitative analysis is conducted to find the redshifted ultrahigh center-of-mass (CM) energy as a result of a two-particle collision specifically near the horizon. The recent Event Horizon Telescope (EHT) triggered a surge of interest in strong gravitational lensing by black holes, which provide a new tool comparing the black hole lensing in general relativity and alternate gravity theories. Motivated by this, we also discussed both strong and weak-field gravitational lensing in the space-time discretely for a uniform plasma and a singular isothermal sphere. We calculated the light deflection coefficients $\overline{a}$ and $\overline{b}$ in the strong field limits, and their variance with the rotational parameter $a$ for different plasma frequency as well as in vacuum. For EBI black holes, we found that plasma's presence increases the photon sphere radius, the deflection angle, the deflection coefficients $\overline{a}$, $\overline{b}$, the angular positions and the angular separation between the relativistic images. It is also shown that with increasing spin the impact of plasma on a strong gravitational lensing becomes smaller as the spin parameter grows in the prograde orbit ($a&gt;0$). For extreme black holes, the strong gravitational effects in the homogenous plasma are similar to those of in a vacuum. We investigate strong gravitational lensing effects by supermassive black holes Sgr A* and M87*. Considering rotating EBI black holes as the lens, we find the angular position of images for Sgr A* and M87* and observe that the deviations of the angular position from that of the analogous Kerr black hole are not more than $2.44\text{ }\text{ }\ensuremath{\mu}\mathrm{as}$ for Sgr A* and $1.83\text{ }\text{ }\ensuremath{\mu}\mathrm{as}$ for M87*, which are unlikely to get resolved by the current EHT observations.

Hypothetical ultralight bosonic fields will spontaneously form macroscopic bosonic halos around Kerr black holes, via superradiance, transferring part of the mass and angular momentum of the black hole into the halo. Such a process, however, is only efficient if resonant—when the Compton wavelength of the field approximately matches the gravitational scale of the black hole. For a complex-valued field, the process can form a stationary, bosonic field black hole equilibrium state—a black hole with synchronised hair. For sufficiently massive black holes, such as the one at the centre of the M87 supergiant elliptic galaxy, the hairy black hole can be robust against its own superradiant instabilities, within a Hubble time. Studying the shadows of such scalar hairy black holes, we constrain the amount of hair which is compatible with the Event Horizon Telescope (EHT) observations of the M87 supermassive black hole, assuming the hair is a condensate of ultralight scalar particles of mass μ ∼ 10 − 20 eV, as to be dynamically viable. We show the EHT observations set a weak constraint, in the sense that typical hairy black holes that could develop their hair dynamically, are compatible with the observations, when taking into account the EHT error bars and the black hole mass/distance uncertainty.

The Event Horizon Telescope will generate horizon scale images of the black hole in the center of the Milky Way, Sgr A*. Image reconstruction using interferometric visibilities rests on the assumption of a stationary image. We explore the limitations of this assumption using high-cadence disk- and jet-dominated GRMHD simulations of Sgr A*. We also employ analytic models that capture the basic characteristics of the images to understand the origin of the variability in the simulated visibility amplitudes. We find that, in all simulations, the visibility amplitudes for baselines oriented parallel and perpendicular to the spin axis of the black hole follow general trends that do not depend strongly on accretion-flow properties. This suggests that fitting Event Horizon Telescope observations with simple geometric models may lead to a reasonably accurate determination of the orientation of the black hole on the plane of the sky. However, in the disk-dominated models, the locations and depths of the minima in the visibility amplitudes are highly variable and are not related simply to the size of the black hole shadow. This suggests that using time-independent models to infer additional black hole parameters, such as the shadow size or the spin magnitude, will be severely affected by the variability of the accretion flow.

The successful observation of M87 supermassive black hole by the Black Hole Event Horizon Telescope(EHT) provides a very good opportunity to study the theory of gravity. In this work, we obtain the exact solution for the short hair black hole (BH) in the rotation situation, and calculate in detail how hairs affect the BH shadow. For the exact solution part, using the Newman-Janis algorithm, we generalize the spherically symmetric short-hair black hole metric to the rotation case (space-time lie element (2.25)). For the BH shadow part, we study two hairy BH models. In model 1, the properties of scalar hair are determined by the parameters α0 and L (We re-obtained the results in reference [48] for the convenience of discussion in this work). In model 2, the scalar hair of the BH is short hair. In this model, the shape of the BH shadow is determined by scalar charge Qm and k. The main results are as follows: (1) In the case of rotational short-hair BH, the value range of parameter k is k > 1 (2.25), the range of short-hair charge value Qm is greatly reduced due to the introduction of the BH spin a. When 0leqslant {Q}_mleqslant frac{2}{3}times {4}^{frac{1}{3}} , the rotational short-hair BH has two event horizons at this time. When {Q}_m>frac{2}{3}times {4}^{frac{1}{3}} , the rotational short-hair BH has three unequal event horizons, so the space-time structure of the BH is significantly different from that of Kerr BH. (2) For model 1, the effect of scalar hair on the BH shadows corresponds to that of ε > 0 in reference [38, 48], but the specific changes of the shadows in model 1 are different. This is because the BH hair in reference [38] is considered as a perturbation to the BH, while the space-time metric of model 1 is accurate and does not have perturbation property. For model 2, that is, the change of the BH shadow caused by short hairs, the main change trend is consistent with that of ε < 0 in reference [38]. Because of the special structure of the short-hair BH, the specific changes of BH shadows are different. (3) the variation of Rs and δs with L and α0 is not a monotone function in model 1, but in model 2, it is. These results show that scalar hairs (model 1) have different effects on Kerr BH shadows than short hairs (model 2), so it is possible to distinguish the types and properties of these hairs if they are detected by EHT observations. (4) as for the effects of the hairs on energy emissivity, the main results in model 1 [48], different energy emissivity curves have intersection phenomenon, while in model 2 (short-hair BH), there is no similar intersection phenomenon. In general, various BH hairs have different effects on the shadows, such as non-monotonic properties and intersection phenomena mentioned in this work. Using these characteristics, it is possible to test the no-hair theorem in future EHT observations, so as to have a deeper understanding of the quantum effect of BHs. In future work, we will use numerical simulations to study the effects of various hairs on BHs and their observed properties.

Detailed and long‐term VLBI (Very Long Baseline Interferometry) studies of the variable jets of supermassive black holes helps us to understand the emission processes of these fascinating phenomena. When observed and traced precisely, jet component kinematics reveals details about the potential motion of the jet base. Following this motion over decades with VLBI monitoring reveals – in some cases – the signatures of precession. While several processes can cause precession, the most likely cause seems to be a supermassive binary black hole in the central region of the AGN. We present examples of the analysis of high‐resolution VLBI observations which provides us with insight into the physics of these objects and reveals evidence for the presence of double black hole cores. EHT (Event Horizon Telescope) observations will probably soon tell us more about the jet origin and launching mechanism at the very centers of nearby active galactic nuclei. An important question to be addressed by the EHT and related observations will be whether Sgr A*, the supermassive black hole in the Galactic Center, has a jet as well. (© 2015 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Unification of gravity with other interactions, achieving the ultimate framework of quantum gravity, and fundamental problems in particle physics and cosmology motivate to consider extra spatial dimensions. The impact of these extra dimensions on the modified theories of gravity has attracted a lot of attention. One way to examine how extra dimensions affect the modified gravitational theories is to analytically investigate astrophysical phenomena, such as black hole shadows. In this study, we aim to investigate the behavior of the shadow shapes of higher-dimensional charged black hole solutions including asymptotically locally flat (ALF) and asymptotically locally AdS (ALAdS) in Einstein–Horndeski–Maxwell (EHM) gravitational theory. We utilize the Hamilton–Jacobi method to find photon orbits around these black holes as well as the Carter approach to formulate the geodesic equations. We examine how extra dimensions, negative cosmological constant, electric charge, and coupling constants of the EHM gravity affect the shadow size of the black hole. Then, we constrain these parameters by comparing the shadow radius of these black holes with the shadow size of M87* supermassive black hole captured by the Event Horizon Telescope (EHT) collaborations. We discover that generally the presence of extra dimensions within the EHM gravity results in reducing the shadow size of higher-dimensional ALF and ALAdS charged black holes, whereas the impact of electric charge on the shadow of these black holes is suppressible. Interestingly, we observe that decreasing the negative cosmological constant, i.e., increasing its absolute value, leads to increase the shadow size of the ALAdS charged higher-dimensional black hole in the EHM gravity. Surprisingly, based on the constraints from EHT observations, we discover that only the shadow size of the four dimensional ALF charged black hole lies in the confidence levels of EHT data, whereas owing to the presence of the negative cosmological constant, the shadow radius of the four, five, and seven dimensional ALAdS charged black holes lie within the EHT data confidence levels.

Context.The Event Horizon Telescope (EHT) has imaged the shadow of the supermassive black hole in M 87. A library of general relativistic magnetohydrodynamics (GMRHD) models was fit to the observational data, providing constraints on black hole parameters.Aims.We investigate how much better future experiments can realistically constrain these parameters and test theories of gravity.Methods.We generated realistic synthetic 230 GHz data from representative input models taken from a GRMHD image library for M 87, using the 2017, 2021, and an expanded EHT array. The synthetic data were run through an automated data reduction pipeline used by the EHT. Additionally, we simulated observations at 230, 557, and 690 GHz with the Event Horizon Imager (EHI) Space VLBI concept. Using one of the EHT parameter estimation pipelines, we fit the GRMHD library images to the synthetic data and investigated how the black hole parameter estimations are affected by different arrays and repeated observations.Results.Repeated observations play an important role in constraining black hole and accretion parameters as the varying source structure is averaged out. A modest expansion of the EHT already leads to stronger parameter constraints in our simulations. High-frequency observations from space with the EHI rule out all but ∼15% of the GRMHD models in our library, strongly constraining the magnetic flux and black hole spin. The 1σconstraints on the black hole mass improve by a factor of five with repeated high-frequency space array observations as compared to observations with the current ground array. If the black hole spin, magnetization, and electron temperature distribution can be independently constrained, the shadow size for a given black hole mass can be tested to ∼0.5% with the EHI space array, which allows tests of deviations from general relativity. With such a measurement, high-precision tests of the Kerr metric become within reach from observations of the Galactic Center black hole Sagittarius A*.

Black hole (BH) shadow observations and gravitational wave astronomy have become crucial approaches for exploring BH physics and testing gravitational theories in extreme environments. This paper investigates the charged black hole with scalar hair (CBH-SH) derived from the Einstein–Maxwell-conformal coupled scalar (EMCS) theory. We first constrain the parameter space $$(Q/M, s/M^2)$$ ( Q / M , s / M 2 ) of the BH using the Event Horizon Telescope (EHT) observations of M87* and Sgr A*. The results show that M87* provides stronger constraints on positive scalar hair, constraining the scalar hair s within $$0\le s/M^2\le 0.4632$$ 0 ≤ s / M 2 ≤ 0.4632 and the charge Q within the range $$0\le Q/M\le 0.6806.$$ 0 ≤ Q / M ≤ 0.6806 . In contrast, Sgr A* imposes tighter constraints on negative scalar hair. When Q approaches zero, s is constrained within the range $$0\ge s/M^2\ge -0.0277.$$ 0 ≥ s / M 2 ≥ - 0.0277 . Overall, EHT observations can provide constraints at most on the order of $${\mathcal {O}}\left( {10}^{-1}\right) .$$ O 10 - 1 . Subsequently, we construct extreme mass ratio inspiral (EMRI) systems and calculate their gravitational waves to assess the detection capability of the LISA detector for these BHs. The results indicate that for central BHs of $$M={10}^6M_\odot ,$$ M = 10 6 M ⊙ , LISA is expected to detect scalar hair $$s/M^2$$ s / M 2 at the $${\mathcal {O}}\left( {10}^{-4}\right) $$ O 10 - 4 level and charge Q/M at the $${\mathcal {O}}\left( {10}^{-2}\right) $$ O 10 - 2 level, with detection sensitivity far exceeding the current EHT capabilities. This demonstrates the immense potential of EMRI gravitational wave observations in testing EMCS theory.

Shadow of Kerr black hole surrounded by a cloud of strings in Rastall gravity and constraints from M87*

The quantum-corrected black hole model demonstrates significant potential in the study of gravitational lensing effects. By incorporating quantum effects, this model addresses the singularity problem in classical black holes. In this paper, we investigate the impact of the quantum correction parameter on the lensing effect based on the quantum-corrected black hole model. Using the black holes M87∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M87^*$$\\end{document} and SgrA∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Sgr A^*$$\\end{document} as our subjects, we explore the influence of the quantum correction parameter on angular position, Einstein ring, and time delay. Additionally, we use data from the Event Horizon Telescope observations of black hole shadows to constrain the quantum correction parameter. Our results indicate that the quantum correction parameter significantly affects the lensing coefficients a¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{a}$$\\end{document} and b¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{b}$$\\end{document}, as well as the Einstein ring. The position θ∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{\\infty }$$\\end{document} and brightness ratio S of the relativistic image exhibit significant changes,with deviations on the order of magnitude of ∼1μas\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 1\\,\\upmu \\! \ extrm{as}$$\\end{document} and ∼0.01μas\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 0.01\\,\\upmu \\! \ extrm{as}$$\\end{document}, respectively. The impact of the quantum correction parameter on the time delay ΔT21\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta T_{21}$$\\end{document} is particularly significant in the M87∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M87^*$$\\end{document} black hole, with deviations reaching up to several tens of hours. Using observational data from the Event Horizon Telescope(EHT) of black hole shadows to constrain the quantum correction parameter, the constraint range under the M87∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M87^*$$\\end{document} black hole is 0≤αM2≤1.4087\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0\\le \\frac{\\alpha }{M^2}\\le 1.4087$$\\end{document} and the constraint range under the SgrA∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Sgr A^*$$\\end{document} black hole is 0.9713≤αM2≤1.6715\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.9713\\le \\frac{\\alpha }{M^2}\\le 1.6715$$\\end{document}. Although the current resolution of the EHT limits the observation of subtle differences, future high-resolution telescopes are expected to further distinguish between the quantum-corrected black hole and the Schwarzschild black hole, providing new avenues for exploring quantum gravitational effects.