In this work, we investigate the shadow properties of the Kerr–Newman–Anti-de Sitter black hole coupled to nonlinear electrodynamics. The shadow is constructed by employing the celestial coordinate approach for an observer located at a finite distance, which is required due to the non-asymptotically flat structure of the spacetime. The size, distortion, area, and oblateness of the shadow are analyzed in terms of the black hole parameters, namely, the spin, the effective charge, and the nonlinearity parameter. We show that the nonlinear electrodynamics significantly modifies the photon region and therefore changes the shadow observables, while the rotation mainly controls the deformation of the silhouette. We further confront the theoretical results with the Event Horizon Telescope observations of M87* and Sgr A* in order to constrain the parameter space of the model. The allowed ranges of the effective charge depend sensitively on the nonlinearity parameter, and the combination of both sources leads to tighter and physically more consistent bounds. In addition, we study the energy emission rate derived from the shadow radius and the Hawking temperature and discuss how it is affected by the rotation and the nonlinear electromagnetic field. Our analysis shows that the considered black hole solution provides a consistent extension of the Kerr geometry in a non-asymptotically flat background and that the shadow observables can be used as an efficient tool to test the effects of nonlinear electrodynamics in strong gravity.

Abstract In this paper, we study the polymer black hole solution surrounded by a quintessence field. The influence of quintessence on the polymer black hole is investigated through its thermodynamic properties, such as the Hawking temperature, entropy, and specific heat, which allow us to address the question of thermodynamic stability. We then calculate bounds on the electromagnetic greybody factors and photon emission rates of the black hole, highlighting the interplay between quintessence and quantum gravity effects in determining these phenomena. We also examine the effects of quintessence and quantum gravity on the geodesics and shadows of massless particles around the black hole. Our results are further compared with observational data of both the Sagittarius A* and M87* black holes from the Event Horizon Telescope (EHT) collaboration.

Abstract We present independent imaging analyses of Event Horizon Telescope (EHT) observations of the active galactic nuclei in radio galaxy Centaurus A and quasar 3C 279 using Generative Deep learning Image Reconstruction with Closure Terms (G en DIR e CT), a recently developed machine-learning framework built on conditional diffusion models that uses interferometric closure invariants as primary observables. For Centaurus A, our reconstruction reveals two prominent emission ridges (≃ 80 μas each) along the jet sheath with a brightness ratio of 1.4 ± 0.1 and an opening angle of 12.3 ± 0.3 deg. For 3C 279, we identify three distinct components in the image, with the southern jet ejecta on sub-parsec scale exhibiting a proper motion of 4.6 ± 1.0 μas over ≈ 5.39 days away from the northern components, corresponding to an apparent superluminal velocity of ≃ 10 ± 2 times light speed. These measurements are consistent with those reported by the EHT Collaboration. The results are significant because we demonstrate that: (1) imaging from interferometric aperture synthesis data, especially in VLBI and most acutely in extremely sparse arrays like the EHT, remains a severely ill-posed and challenging inverse problem, yet closure invariants preserve robust morphological information that can strongly constrain structural features, and (2) more importantly, closure-invariant imaging largely avoids calibration systematics, thus providing a fundamentally independent view of spatial structure with very high angular resolution. The generative nature of G en DIR e CT further allows us to sample and characterise clusters of plausible image solutions for each dataset. As a calibration-independent, generative imaging approach, G en DIR e CT offers a robust and truly independent blind-imaging tool for current and future VLBI experiments.

Abstract We investigate a rotating black hole embedded in a five-dimensional flat bulk by extending the Kerr metric through the Gürses-Gürsey line element. Employing Boyer-Lindquist coordinates, we reinterpret the black hole as a charged-like object in five dimensions and analyze its horizon structure and shadow morphology. Our results reveal that the shadow is shaped by an axially symmetric gravitational field modulated by an extrinsic curvature term arising from the higher-dimensional embedding. Simulations demonstrate that the visibility amplitude and shadow profile of the Gürses-Gürsey black hole align with Event Horizon Telescope observations of $$\hbox {M87}^{*}$$ M87 ∗ in the Kerr limit, while also allowing measurable deviations that could be probed by future high-resolution experiments.

Abstract We investigate how deviations from the Bekenstein–Hawking entropy modify black-hole spacetimes through the recently proposed entropy-geometry correspondence. For four representative modified entropies, namely Barrow, Rényi, Kaniadakis, and logarithmic, we derive the corresponding effective metrics and analyze their thermodynamic and topological classification using the off-shell free energy and winding numbers. We show that Barrow and Rényi entropies yield a single unstable sector with global charge $$W=-1$$ W = - 1 , while logarithmic and Kaniadakis corrections produce canceling defects with $$W=0$$ W = 0 , revealing topological structures absent in the Schwarzschild case. Using the modified metrics, we further calculate the photon-sphere radius and shadow size, showing that each modified entropy relation induces characteristic optical shifts. Thus, by comparing with Event Horizon Telescope observations of Sgr A $$^*$$ ∗ , we extract new bounds on all entropy-deformation parameters. Our results demonstrate that thermodynamic topology, together with photon-sphere phenomenology, offers a viable way to test generalized entropy frameworks and probe departures from the Bekenstein-Hawking area law.

Abstract The main goal of this work is to investigate how relevant quantum gravity corrections can be, at an effective level, in the geometry describing the exterior of a black hole, and whether such corrections can be tested observationally. For this purpose, we employ Bozza's method to calculate the deflection angle of light in presence of the strong gravitational field generated by an improved Schwarzschild-like black hole whose metric, regular throughout the entire spacetime, was derived using the improved Generalized Uncertainty Principle (GUP). This framework incorporates effective quantum gravity corrections that resolve the physical singularity inside the black hole, quantified by a model parameter | Qc |. In addition, the event horizon, the photon sphere, and the shadow radius receive modifications characterized by a second model parameter Qb . Using observational properties of the supermassive black holes Messier 87* and Sagittarius A * reported by the Event Horizon Telescope, we derive constraints on the parameter | Qb |, namely 0 ≤ | Qb | ≤ 0.3. To the best of our knowledge, these are the first constraints reported in the literature for this improved GUP parameter. Since | Qc | does not play a significant role in the correction of the shadow radius, it was not possible to impose restrictions on its allowed values, however, it is important to consider a non-zero | Qc | in order to avoid a black hole singularity.

Black holes are among the most compelling predictions of general relativity (GR) and are now strongly supported by observations from gravitational-wave detectors and the Event Horizon Telescope (EHT). While standard black hole solutions suffer from central singularities, regular black holes avoid this issue by introducing a nonsingular core. In this work, we extend the Dymnikova regular black hole to higher dimensions using a smooth matter distribution. The resulting spacetime features a de Sitter-like core and two horizons. We analyze photon motion and show that circular photon orbits remain unstable, giving rise to a well-defined black hole shadow. Our results indicate that the shadow size grows with the black hole scale but decreases slightly as the number of dimensions increases. We also investigate thermodynamic properties, including Hawking temperature and energy emission, and find a strong dependence on dimensionality. Finally, we compare our model with EHT observations to place constraints on the parameters and highlight potential observational signatures of higher-dimensional regular black holes.

Abstract Very long baseline interferometry (VLBI) achieves the highest angular resolution in astronomy. VLBI measures corrupted Fourier components, known as visibilities. Reconstructing on-sky images from these visibilities is a challenging inverse problem, particularly for sparse arrays such as the Event Horizon Telescope (EHT) and the Very Long Baseline Array, where incomplete sampling and severe calibration errors introduce significant uncertainty in the image. To help guide convergence and control the uncertainty in image reconstructions, regularization on the space of images is utilized, such as enforcing smoothness or similarity to a fiducial image. Coupled with this regularization is the introduction of a new set of parameters that modulate its strength. We present a hierarchical Bayesian imaging approach (hierarchical interferometric Bayesian Imaging, HIBI) that enables the quantification of uncertainty for all parameters. Incorporating instrumental effects within HIBI is straightforward, allowing for simultaneous imaging and calibration of data. To showcase HIBI’s effectiveness and flexibility, we build a simple imaging model based on Markov random fields and demonstrate how different physical components can be included, e.g., black hole shadow size, and their uncertainties can be inferred. For example, while the original EHT publications were unable to constrain the ring width of M87*, HIBI measures a width of 9.3 ± 1.3 μ as. We apply HIBI to image and calibrate EHT synthetic data, real EHT observations of M87*, and multifrequency observations of OJ 287. Across these tests, HIBI accurately recovers a wide variety of image structures and quantifies their uncertainties. HIBI is publicly available in the Comrade VLBI software repository.

We investigate weak gravitational lensing and shadow properties of the Konoplya-Zhidenko black hole surrounded by perfect fluid dark matter and a plasma medium. Considering both homogeneous and non-homogeneous (singular isothermal sphere) plasma distributions, we analyze how the dark matter, the deformation parameter, and plasma frequency modify the deflection angle of light rays and black hole’s shadow radius. Our results show that plasma enhances light bending and reduces the shadow size, with the largest shadow in vacuum, followed by non-homogeneous plasma, and the smallest in homogeneous plasma. Comparison with Event Horizon Telescope observations of Sgr A* constrains the allowed parameter space, linking theoretical predictions to measured shadow radii. Additionally, we study Hawking temperature, specific heat, and Gibbs free energy, revealing the roles of perfect fluid dark matter and spacetime deformation in black hole stability and phase behavior. This analysis provides insights into the observational signatures and thermodynamic properties of deformed black holes embedded in realistic galactic environments.

In this paper I present a case study of the creation of the Event Horizon Telescope (EHT), which provided the first image of a black hole shadow (April 2019) and that of the central black hole of the Milky Way (May 2022), as one in which the collaborative approach was primarily motivated by strong epistemic needs. To this end, I introduce and explore the notion of "epistemic constraint," meaning any component of the world that prevents us from gaining some definite kind of knowledge in a specific manner and allows or promotes some other specific kind of knowledge in defined ways. The collaborative approach that led to the recent images of black hole shadows through the EHT is described in terms of "epistemically constrained collaboration" - i.e., a collaborative mode of research where the epistemic constraints prevail over other factors - and the most important features of this concept are expounded.

Abstract In this paper we study the shadow and quasi-normal modes (QNMs) of a black hole (BH) surrounded by a dark matter halo with Hernquist-type density distribution, which was reported in Cardoso et al. (Phys. Rev. D 105(6):L061501, 2022). In astrophysical scenarios, we find that the shadow radius enlarges as the compactness of halo increases. Therefore, we obtain an upper bound for the compactness $$\mathcal{C}\le 0.092$$ C ≤ 0.092 with the Event Horizon Telescope (EHT) observations. We calculate axial gravitational QNMs of the galactic BH up to $$\mathcal{C}\sim \mathcal{O}(1)$$ C ∼ O ( 1 ) , and fit the redshift relative to Schwarzschild QNMs up to second order in the compactness (for $$\mathcal{C}\le 0.3)$$ C ≤ 0.3 ) . These highly redshifted QNMs, resulting from large compactness, are key to modeling the dark matter halo.

Abstract We study synchrotron polarization in spatially resolved horizon-scale images, such as those produced by the Event Horizon Telescope (EHT). In both general relativistic magnetohydrodynamic (GRMHD) simulations and simplified models of the black hole magnetosphere, the polarization angle, quantified by the complex observable ∠β 2 , depends strongly and systematically on the black hole spin. This relationship arises from the coupling between spin and the structure of the magnetic field in the emission region, and it can be computed analytically in the force-free limit. To explore this connection further, we develop a semianalytic inflow framework that solves the time-stationary axisymmetric equations of GRMHD in the black hole’s equatorial plane; this model can interpolate between the force-free and inertial regimes by varying the magnetization of the inflow. Our model demonstrates how finite inertia modifies the structure of the electromagnetic field and can be used to quantitatively predict the observed polarization pattern. By comparing reduced models, GRMHD simulations, and analytic limits, we show that the observed synchrotron polarization can serve as a robust diagnostic of spin under assumptions about Faraday rotation and the emission geometry. Applied to EHT data, the model disfavors high-spin configurations for both M87 ∗ and Sgr A ∗ , highlighting the potential of polarimetric imaging as a probe of both black hole spin and near-horizon plasma physics.

Sagittarius A* ( exhibits frequent flaring activity across the electromagnetic spectrum that is often associated with a localized region of strong emission known as a hot spot. We aim to establish an empirical relationship linking key parameters of this phenomenon -- emission radius, inclination, and black hole spin -- to the observed angle difference between the primary and secondary image (Δ PA) that an interferometric array could resolve. Using the numerical radiative transfer code we generated a library of more than 900 models with varying system parameters and computed the position angle difference on the sky between the primary and secondary images of the hot spot. The key assumptions are equatorial and circular orbits. For these models we find that the average Δ PA over a full period is insensitive to inclination. This result significantly simplifies potential spin measurements, which might otherwise depend strongly on inclination. Additionally, we derived a relation connecting spin to Δ PA, given the period and emission radius of the hot spot, with an accuracy of better than 5^̧irc in most cases. Finally, we present a mock observation to showcase the potential of this relation for spin inference. Our results provide a novel approach for black hole spin measurements using high-resolution observations, such as future movies of Sgr A* obtained with the Event Horizon Telescope, the next-generation Event Horizon Telescope, and the Black Hole Explorer. Although discrepancies will likely arise in the general case (lifting model assumptions), the methodology is sound, and easily extendable.

Black hole jets represent one of the most extreme manifestations of astrophysical processes, linking accretion physics, relativistic magnetohydrodynamics, and large-scale feedback in galaxies and clusters. Despite decades of observational and theoretical work, the mechanisms governing jet launching, collimation, and energy dissipation remain open questions. In this article, we discuss how upcoming facilities such as the Event Horizon Telescope (EHT), the Cherenkov Telescope Array (CTA), the Vera C. Rubin Observatory (LSST), and the Whole Earth Blazar Telescope (WEBT) will provide unprecedented constraints on jet dynamics, variability, and multi-wavelength signatures. Furthermore, we highlight theoretical challenges, including the role of magnetically arrested disks (MADs), plasma microphysics, and general relativistic magnetohydrodynamic (GRMHD) simulations in shaping our understanding of jet formation. By combining high-resolution imaging, time-domain surveys, and advanced simulations, the next decade promises transformative progress in unveiling the physics of black hole jets.

Context. Magnetic fields play a pivotal role in the dynamics of black hole accretion flows and in the formation of relativistic jets. Observations by the Event Horizon Telescope (EHT) provided unprecedented insights into accretion structures near black holes. Interpreting these observations requires a theoretical framework that links polarized emission to the underlying system properties and magnetic field geometries. Aims. We investigated how the system properties, in particular, the magnetic field geometry in the region of the event horizon scale, affect the structure of the observable synchrotron emission in M 87*. Specifically, we characterized the sensitivity of observables used by the EHT to black hole spin, plasma dynamics, accretion disk thickness, and magnetic field geometry. Methods. We adopted a semi-analytic radiatively inefficient accretion flow model in Kerr spacetime. We varied the magnetic field geometry, black hole spin, accretion disk dynamics, and geometric thickness of the disk. We performed general relativistic ray-tracing with a full polarized radiative transfer to obtain synthetic images of M 87*. We extracted EHT observables, such as disk diameter, asymmetry, and polarimetric metrics from synthetic models. We also considered a number of general relativistic magnetohydrodynamics simulations and compared them with the semi-analytical models. Results. The effect of the disk thickness on the observables is limited. On the other hand, magnetic configurations dominated by the toroidal and poloidal fields can be distinguished reliably. The flow dynamics, in particular, radial inflow, also significantly affects the EHT observables. Conclusions. The M 87* system is most consistent with a flow dominated by the poloidal magnetic field with partially radial inflow. While the spin remains elusive, moderate or high positive values are preferred.

We analyze the observational features of hot-spots orbiting parametrized black hole (BH) spacetimes. We select a total of four BH spacetimes, two of them adapted from the Johanssen-Psaltis (JP) parametrization, and two from the Konoplya-Rezzolla-Zhidenko (KRZ) parametrization, corresponding to the most extreme configurations whose shadow sizes are within the 2σ-constraints of the Event Horizon Telescope (EHT). We use the ray-tracing software GYOTO to simulate the orbit of a spherically symmetric hot-spot emitting synchrotron radiation close to a central parametrized BH object, in a vertical magnetic field configuration, and we extract the corresponding astrometric and polarimetric observables for the Stokes parameters I, Q and U, namely the time integrated fluxes, temporal fluxes and magnitudes, temporal centroid, temporal QU-loops, and temporal Electric Field Position Angle (EVPA). Our results indicate that at low inclination the astrometric observables extracted from the parametrized BH spacetimes considered are qualitatively similar to those extracted from the Schwarzschild one, with minor quantitative deviations caused by differences in the size and position of the secondary images. On the other hand, the polarimetric observables at high inclination present qualitative differences, but these are only visible for a short portion of the whole hot-spot orbit. Furthermore, the observables extracted from the JP parametrized BH models deviate more prominently from those of the Schwarzschild model than the ones extracted from the KRZ parametrized BH models, with the JP model with a positive free parameter deviating the most among all models tested. Given the strong similarity among the observables extracted from all models tested, we point out that more precise observations are needed to successfully impose constraints on parametrized BH models via this method.

Abstract In this work, we study a special form of Horndeski solutions, viz. quartic “square-root” Horndeski black hole immersed in a perfect-fluid dark-matter halo, by examining its thermodynamics, null-geodesic shape, optical shadow, and quasinormal ringdown spectrum. The model is characterized by three parameters, namely $$\beta $$ β , $$\eta $$ η (non-minimal Horndeski coupling parameters), and b (perfect fluid dark matter parameter), which collectively determine horizon properties and observational effects. To study thermodynamic stability, we used the specific-heat and free-energy arguments, with which we demonstrated that small-horizon states are locally stable but are never globally preferred. Analytic solutions of null geodesics reveal the radius of the photon sphere and the critical impact parameter, proving that increases in the dark matter parameters and the Horndeski parameter $$\beta $$ β enlarge both the photon sphere and the subsequent shadow, whereas increase in the Horndeski coupling $$\eta $$ η causes a mild diminishing in the shadow radius. Numerical ray tracing verifies these qualitative trends in the apparent shadow. Using the 6 $$^{th}$$ th - order WKB approximation method, we also calculate the scalar quasinormal modes and determine that oscillation frequencies and damping rates behave oppositely according to the sign and magnitude of each parameter. By comparing the shadow radius with the recent Event Horizon Telescope constraints on the Sgr A*, we find a narrow window of parameter space that agrees with observed data. In other words, the coupling parameters should be very small. These measurements restrict modified gravity impacts within realistic astrophysical contexts.

Abstract Using very-long-baseline interferometry (VLBI) observations at (sub)millimeter wavelengths, the Event Horizon Telescope (EHT) currently achieves the finest angular resolution of any astronomical facility, necessary for imaging the horizon-scale structure around supermassive black holes. A significant calibration challenge for high-frequency VLBI stems from rapid variations in the atmospheric water vapor content above each telescope in the array, which induce corresponding fluctuations in the phase of the correlated signal that limit the coherent integration time and thus the achievable sensitivity. In this paper, we introduce a model that describes station-based phase corruptions jointly with a parameterization for the source structure. We adopt a Gaussian process (GP) prescription for the time evolution of these phase corruptions, which provides sufficient flexibility to capture even highly erratic phase behavior. The use of GPs permits the application of a Kalman filtering algorithm for numerical marginalization of these phase corruptions, which permits efficient exploration of the remaining parameter space. Our model also removes the need to specify an arbitrary “reference station” during calibration, instead establishing a global phase zero-point by enforcing the GPs at all stations to have fixed mean and finite variance. We validate our method using a real EHT observation of the blazar 3C 279, demonstrating that our approach yields calibration solutions that are consistent with those determined by the EHT Collaboration. The model presented here can be straightforwardly extended to incorporate frequency-dependent phase behavior, such as is relevant for the frequency phase transfer calibration technique.

Abstract Recent imaging of supermassive black holes by the Event Horizon Telescope has relied on exhaustive parameter-space searches, matching observations to large, precomputed libraries of theoretical models. As observational data become increasingly precise, the limitations of this computationally expensive approach grow more acute, creating a pressing need for more efficient methods. In this work, we present Jipole , an automatically differentiable (AD), ipole -based code for radiative transfer in curved spacetimes, designed to compute image gradients with respect to underlying model parameters. These gradients quantify how parameter changes—such as the black hole’s spin or the observer’s inclination—affect the image, enabling more efficient parameter estimation and reducing the number of required images. We validate Jipole against ipole in two analytical tests and then compare pixelwise intensity derivatives from AD with those from finite-difference methods. We then demonstrate the utility of these gradients by performing parameter recovery for an analytical model in three increasingly complex cases for the injected image: ideal, blurred, and blurred with added noise. In most cases, high-accuracy fits are obtained in only a few optimization steps, failing only in cases with extremely low signal-to-noise ratios. These results highlight the potential of AD-based methods to accelerate robust, high-fidelity model-data comparisons in current and future black hole imaging efforts.

We investigate the presence and spatial characteristics of the jet base emission in M87* at $230 GHz $, enabled by the significantly enhanced ̆v coverage in the 2021 Event Horizon Telescope (EHT) observations. The integration of the 12 Kitt Peak Telescope (USA) and NOEMA (France) stations into the array introduces two critical intermediate-length baselines to SMT (USA) and IRAM 30 (Spain), providing sensitivity to emission structures at spatial scales of ∼ 250 μ as and ∼ 2500 μ as (∼ 0.02 pc and ∼ 0.2 pc ). Without these new baselines, previous EHT observations of the source in 2017 and 2018 lacked the capability to constrain emission on large scales, where a ``missing flux" of order ∼ 1,Jy is expected to reside. To probe these scales, we analyzed closure phases---robust against station-based gain calibration errors---and model the jet base emission using a simple Gaussian component offset from the compact ring emission at spatial separations $> 100 μ as $. Our analysis revealed a Gaussian feature centered at (Δ R.A. ≈ 320 μ as Δ Dec. ≈ 60 μ as ), projected separation of ≈ 5500 AU with an estimated flux density of only ∼ 60 mJy implying that most of the missing flux identified in previous EHT studies had to originate from different, larger scales. Brighter emission at the relevant spatial scales is firmly ruled out, and the data do not favor more complex models. This component aligns with the inferred position of the large-scale jet and is therefore physically consistent with the emission of the jet base. While our findings point to detectable jet base emission at $230 GHz $, the limited coverage provided by only two intermediate baselines limits our ability to robustly reconstruct its morphology. Consequently, we treated the recovered Gaussian as an upper limit on the jet base flux density. Future EHT observations with expanded intermediate baseline coverage will be essential to constrain the structure and nature of this component with higher precision.