Thanks for the releasing image of supermassive black holes (BHs) by the event horizon telescope (EHT) at the heart of the M87 galaxy. After the discovery of this mysterious object, scientists paid attention to exploring the BH shadow features under different gravitational backgrounds. In this scenario, we study the light rings and observational properties of BH shadow surrounded by different accretion flow models and then investigate the effect of model parameters on the observational display and space-time structure of BHs in the framework of our considering system. Under the incompatible configuration of the emission profiles, the images of BHs comprise that the observed luminosity is mainly determined by direct emission, while the lensing ring will provide a small contribution of the total observed flux and the photon ring makes a negligible contribution due to its exponential narrowness. More importantly, the observed regions and specific intensities of all emission profiles are changed correspondingly under variations of parameters. For optically thin accreting matters, we analyze the profile and specific intensity of the shadows with static and infalling accretions models, respectively. We find that with an infalling motion the interior region of the shadows will be darker than the static case, due to the Doppler effect of the infalling movement. Finally, it is concluded that these findings support the fact that the change of BH state parameters will change the way of space-time geometry, thus affecting the BH shadow dynamics.

In this article, we try to capture the influence of deviation from standard Kerr black hole (BH) spacetime on observed high-frequency quasi-periodic oscillations (QPOs) signal. We explore the dynamics of test particles in the field of rotating compact objects governed by the various modifications of the standard Kerr BH spacetime and apply the model of epicyclic oscillations of Keplerian discs to the observed microquasars and active galactic nuclei high-frequency QPOs data. We present a generalized formalism for fitting two well-known high-frequency QPO models: the epicyclic resonance model and the relativistic precession model. This is done assuming stationary, axisymmetric, and asymptotically flat spacetimes. Recently, we have used the same set of stationary, axisymmetric, and asymptotically flat spacetimes, and estimated the restrictions of spacetime parameters with the help of hot-spot data of three flares observed at Sgr A* by GRAVITY instrument (Misbah Shahzadi et al 2022 Eur. Phys. J. C 82 407). The aim of this work is not to test a particular theoretical model or to determine and constrain its parameters, but to map a set of well-astrophysically motivated deviations from classical Kerr BH spacetime and demonstrate which ones provide the best fit for high-frequency QPOs data and could be fruitful for future exploration.

This paper is devoted to the study of warm inflation using vector fields in the background of a locally rotationally symmetric Bianchi type I model of the universe. We formulate the field equations, and slow-roll and perturbation parameters (scalar and tensor power spectra as well as their spectral indices) in the slow-roll approximation. We evaluate all these parameters in terms of the directional Hubble parameter during the intermediate and logamediate inflationary regimes by taking the dissipation factor as a function of the scalar field as well as a constant. In each case, we calculate the observational parameter of interest, i.e., the tensor–scalar ratio in terms of the inflaton. The graphical behavior of these parameters shows that the anisotropic model is also compatible with WMAP7 and the Planck observational data.

Here we provide shadow images of a Kerr-like black hole (BH) in cold dark matter (CDM) halo illuminated with a celestial light source and a thin accretion disk. The impact of spin parameter a, critical density ρ_c and the scale radius R_s on the observed images of BHs is carefully addressed. The results indicate that as a increases, the circular orbits are shifted rightwards, while the larger values of both ρ_c and R_s are the cause to enhance the radius of circular orbits of the BH shadow. In the case of the celestial light source, the impact of ρ_c on shadow distortion is negligible, but this influence is relatively smaller and becomes appreciable when the parameter R_s has larger values. Next, we discuss the intensity and the size of the inner shadow, which are gradually increasing with the increase of both ρ_c and R_s . On the other hand, in the case of retrograde flow, the intensity of the shadow images significantly decreases, and a crescent moon emerges on the upper right side of the screen. Subsequently, the distinctive features of red-shift factors for direct and lensed images with prograde and retrograde flows are discussed. The outcomes indicate that the distribution of red-shift factors and the optical appearance are closely related to the behaviour of accreting flow as well as with relevant parameters. Using the recent observational data of EHT, we found that the shadow's angular diameter of Sgr A* provides the best-fit parameter constraints as compared to M87*.

The light passing near the black hole (BH) is deflected due to the gravitational effect, producing the BH shadow, a dark inner region that is often surrounded by a bright ring, whose optical appearance comes directly from BH’s mass and its angular momentum. We mainly study the shadow and observable features of non-commutative (NC) charged Kiselev BH, surrounded by various profiles of accretions. To obtain the BH shadow profile, we choose specific values of the model parameters and concluded that the variations of each parameter directly vary the light trajectories and size of BH. For thin disk accretion, which includes direct lensing and photon rings emissions, we analyze that the profile of BH contains the dark interior region and bright photon ring. However, their details depends upon the emissions, generally, direct emission plays significant role in the total observed luminosity, while lensing ring has a small contribution and the photon ring makes a negligible contribution, as usual, the latter can be ignored safely. Moreover, we also consider the static and infalling accretion matters and found that the location of the photon sphere is almost the same for both cases. However, the specific intensity which is observed from BH profile found to be darker for infalling accretion case due to the Doppler effect of the infalling motion as compared to the static one.