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This study investigates the astronomical implications of the Ghosh-Kumar rotating Black Hole (BH), particularly its behaviour on shadow images, illuminated by celestial light sources and equatorial thin accretion disks. Our research delineates a crucial correlation between dynamics of the shadow images and the parameters $a$,~ $q$ and the $\theta_{obs}$, which aptly reflect the influence of the model parameters on the optical features of shadow images. Initially, elevated behavior of both $a$ and $q$ transforms the geometry of the shadow images from perfect circles to an oval shape and converges them towards the centre of the screen. By imposing the backward ray-tracing method, we demonstrate the optical appearance of shadow images of the considering BH spacetime in the celestial light source. The results demonstrate that the Einstein ring shows a transition from an axisymmetric closed circle to an arc-like shape on the screen as well as producing the deformation on the shadow shape with the modifications of spacetime parameters at the fixed observational position. Next, we observe that the attributes of accretion disks along with the relevant parameters on the shadow images are illuminated by both prograde and retrograde accreting flow. Our study reveals the process by which the accretion disk transitions from a disk-like structure to a hat-like shape with the aid of observational angles. Moreover, with an increase of $q$, the observed flux of both direct and lensed images of the accretion disk gradually moves towards the lower zone of the screen. Furthermore, we present the intensity distribution of the redshift factors on the screen. Our analysis suggests that the observer can see both redshift and blueshift factors on the screen at higher observational angles, while augmenting the values of both $a$ and $q$, enhancing the effect of redshift on the screen., Comment: 20 pages, 12 figures

We study the Einstein images of a charged Rastall AdS black hole (BH) within the fabric of AdS/CFT correspondence. Considering the holographic setup, we analyze the amplitude of the total response function for various values of model parameters. With an increase in parameter $\lambda$ and temperature $T$, the amplitude of the response function is decreased, while it is increased with the increase of the electric charge $e$ and chemical potential $\mu$. The influence of frequency $\omega$ also plays an important role in the bulk field, as it is found that the decreasing $\omega$ leads to an increase in the periods of the waves, which means that the amplitude of the response function also depends on the wave source. The relation between $T$ to the inverse of the horizon $r_{h}$ for the parameter $\lambda$ is interpreted under fixed values of other involved parameters. These, in turn, affect the behavior of the response function and the Einstein ring, which may be used to differentiate the present work from previous studies. Via a special optical system, we construct the holographic images of the BH in bulk. The obtained results show that the Einstein ring always appears with concentric stripes at the position of the north pole, and this ring transforms into the luminosity-deformed ring or bright light spot when the distant observer lies away from the north pole. Moreover, from the brightness profiles, it is observed that as $\lambda$ grows, the shadow radius is significantly decreased, while the brightness of the ring is negligibly changed. We further investigate the influence of $T$ and $\mu$ on the ring radius. These results reveal that the increasing values of $T$ lead to an increase in the shadow radius and decrease as the values of $\mu$ grow. Finally, we finish this work with a discussion of the Einstein ring radius obtained by geometric optics, which is consistent with wave optics., Comment: 20 pages, 18 figures

This research paper used a newly proposed strategy for finding the exact inflationary solutions to the Friedman equations in the context of Rastall theory of gravity (RTG), which is known as constant-roll warm inflation (CRWI). The dissipative effects produced during WI are studied by introducing a dissipation factor $Q=\frac{\Gamma}{3H}$, where $\Gamma$ is the coefficient of dissipation. We establish the model to evaluate the inflaton field, effective potential requires to produce inflation, and entropy density. These physical quantities lead to developing the important inflationary observables like scalar/tensor power spectrum, scalar spectral index, tensor-to-scalar ratio, and running of spectral-index for two choices of obtained potential that are $V_0=0$ and $V_0\neq0$. In this study, we focus on the effects of the theory parameter $\lambda$, CR parameter $\beta$, and dissipation factor $Q$ (under a high dissipative regime for which $Q=$constant) on inflation and are constrained to observe the compatibility of our model with Planck TT+lowP (2013), Planck TT, TE, EE+lowP (2015), Planck 2018 and BICEP/Keck 2021 bounds. The results are feasible and interesting up to the $2\sigma$ confidence level. Finally, we conclude that the CR technique produces significant changes in the early universe., Comment: 15 Pages, 13 Figures

With the help of AdS/CFT correspondence, we analyze the holographic Einstein images via the response function of the complex scalar field as a probe wave on the AdS Schwarzschild scalar-tensor-vector gravity (STVG) black hole (BH). We find that the amplitude of the response function $|\langle O\rangle|$ decreases with the increasing values of the coupling parameter $\alpha$, while it increases with the decreasing values of temperature $T$. The frequency $\omega$ of the wave source also plays a significant role in wave periods, as we increase the values of $\omega$, we find a decrease in periods of waves, which means that the total response function closely depends on the wave source. Further, we investigate the optical appearance of the holographic images of the BH in bulk. We found that the holographic ring always appears with the concentric stripe surrounded when the observer is located at the north pole, and an extremely bright ring appears when the observer is at the position of the photon sphere of the BH. With the change of the observational angle, this ring will change into a luminosity-deformed ring or a bright light spot. The corresponding brightness profiles show that the luminosity of the ring decreases, and the shadow radius increases with increasing values of $\alpha$. The relation between temperature $T$ and the inverse of the horizon $h_{e}$ is discussed, which shows the smaller values at the beginning of the horizon $h_{e}$, and then increases as the horizon radius increases. This effect can be used to distinguish the STVG BH solution from other BH solutions. Moreover, these significant features are also reflected in the Einstein ring and the corresponding brightness profiles. In addition, we compare the results obtained by wave optics and geometric optics, which are aligned well, implying that the holographic scheme adopted in this paper is valid., Comment: 19 pages, 19 figures

In this paper, we explore the chaotic signatures of the geodesic dynamics for particles moving in the slowly rotating Hartle-Thorne spacetime; an approximate solution of vacuum Einstein field equations describing the exterior of a massive, deformed, and slowly rotating compact object. We employ the numerical study to examine the geodesics of prolate and oblate deformations for generic orbits and find the plateaus of the rotation curve, which are associated with the existence of Birkhoff islands in the Poincare surface of the section, where the ratio of the radial and polar frequency of geodesics remains constant throughout the island. We investigate various phase space structures, including hyperbolic points and chaotic regions in the neighborhood of resonant islands. Moreover, chaotic behavior is observed to be governed by the stickiness phenomenon, where chaotic orbits remain attached to stable ones for an extended duration before eventually diverging and are attracted toward the surface of the neutron star. The precision of the numerical integration used to simulate the particle's trajectories plays a crucial role in the structures of the Poincare surface of the section. We present a comparison of several efficient structure-preserving numerical schemes of order four applied to the considered non-integrable dynamical system and we investigate which schemes possess the canonical property of the Hamiltonian flow. Among the class of non-symplectic integrators, we employ the explicit Runge-Kutta method and explicit general linear method with a standard projection technique to project the numerical solution onto the desired manifold. The projection scheme admits the integration without any drift from the desired manifold and is computationally cost-effective. We are concerned with two crucial aspects -- long-term behaviour and CPU time consumption., Comment: 21 pages, 12 figures

In this article, we try to capture the influence of deviation from standard Kerr black hole spacetime on observed high-frequency quasi-periodic oscillations signal. We explore the dynamics of test particles in the field of rotating compact objects governed by the various modifications of the standard Kerr black hole spacetime and apply the model of epicyclic oscillations of Keplerian discs to the observed microquasars and active galactic nuclei high-frequency quasi-periodic oscillations data. We presented a generalized formalism for the fitting of the high-frequency quasi-periodic oscillations models so-called epicyclic resonance and relativistic precession models, under the assumption of 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 \citep{Shahzadi-et-al:2022:EPJC:}. 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 black hole spacetime and demonstrate which ones provide the best fit for high-frequency quasi-periodic oscillations data and could be fruitful for future exploration., Comment: 19 pages, 6 figures, 1 table

In the context of holography, the Einstein ring of an AdS black hole (BH) in massive gravity (MG) is depicted. An oscillating Gaussian source on one side of the AdS boundary propagates in bulk, and we impose a response function to explain it. Using a wave optics imaging system, we obtain the optical appearance of the Einstein ring. Our research reveals that the ring can change into a luminosity-deformed ring or light spots depending on the variation of parameters and observational positions. When observers are positioned at the north pole, the holographic profiles always appear as a ring with concentric stripe surroundings, and a bright ring appears at the location of the photon sphere of the BH. These findings are consistent with the radius of the photon sphere of the BH, which is calculated in geometrical optics. Our study contributes to a better understanding of the analytical studies of holographic theory, which can be used to evaluate different types of BHs for a fixed wave source and optical system., Comment: 15 pages, 14 figures

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 in a static case, due to the Doppler effect of the infalling movement. Finally, it is concluded that these findings support that the change of BH state parameters will change the way of space-time geometry, thus affecting the BH shadows dynamics., Comment: 16 pages, 9 figures

In this work, we explore the phenomenon of cosmic evolution using curved FLRW space-time bounded by apparent horizon with a specific holographic cut-off. To this end, we use the framework of Rastall gravity (RG) and universe is assumed to be consists of interacting/ non-interacting dark energy (DE) and dark matter (DM). In both scenarios, we evaluate exact solutions of the dynamical equations and constraint the holographic parameter $c^{2}(z)$ assuming a slowly varying function of red-shift during non-interacting model. For interacting model, we consider $c^{2}$ as a constant function of red-shift. Moreover, we analyze nature of the obtained results via deceleration parameter $(q)$, statefinder pair $(j,s)$ and $Om(z)$-diagnostic by constraining the involved model parameters using latest observational data. The graphical analysis showed that interacting model is very close to $\Lambda$ cold DM ($\Lambda$CDM) model as compared to non-interacting case. We conclude that this holographic proposal is enough to describe the cosmic evolution at an accelerating rate., Comment: 27 pages, 11 figures

This paper is aimed to study the compelling issue of cosmic inflation during rapid oscillations using the framework of non-minimal derivative coupling. To this end, an anisotropic and homogeneous Bianchi I background is considered. In this context, I developed the formalism of anisotropic oscillatory inflation and found some constraints for the existence of inflation. In this era, the parameters related to cosmological perturbations are evaluated, further, their graphical trajectories are presented to check the compatibility of the model with the observational data (Planck 2015 probe), Comment: 24 pages, 11 figures. arXiv admin note: text overlap with arXiv:1309.2932 by other authors

This paper explores the dynamics of warm intermediate and logamediate inflationary models during weak dissipative regime with a general form of dissipative coefficient. We analyze these models within the framework of locally rotationally symmetric Bianchi type I universe. In both cases, we evaluate solution of inflaton, effective scalar potential, dissipative coefficient, slow-roll parameters, scalar and tensor power spectra, scalar spectral index and tensor to scalar ratio under slow-roll approximation. We constrain the model parameters using recent data and conclude that anisotropic inflationary universe model with generalized dissipation coefficient remains compatible with WMAP9, Planck and BICEP2 data., Comment: 24 pages, 12 figures. arXiv admin note: text overlap with arXiv:1312.3502 by other authors

We consider an inflationary universe model in the context of generalized cosmic Chaplygin gas by taking matter field as standard and tachyon scalar fields. We evaluate the corresponding scalar fields and scalar potentials during intermediate and logamediate inflationary regimes by modifying the first Friedmann equation. In each case, we evaluate the number of e-folds, scalar as well as tensor power spectra, scalar spectral index and important observational parameter, i.e., tensor-scalar ratio in terms of inflatons. The graphical behavior of this parameter shows that the model remains incompatible with WMAP7 and Planck observational data in each case., Comment: 20 pages, 8 figures, Accepted for publication in EPJC

This paper is devoted to check the validity of laws of thermodynamics for Kaluza-Klein universe in the state of thermal equilibrium, composed of dark matter and dark energy. The generalized holographic dark energy and generalized Ricci dark energy models are considered here. It is proved that the first and generalized second law of thermodynamics are valid on the apparent horizon for both of these models. Further, we take a horizon of radius $L$ with modified holographic or Ricci dark energy. We conclude that these models do not obey the first and generalized second law of thermodynamics on the horizon of fixed radius $L$ for a specific range of model parameters., Comment: 14 pages, 1 figure

This paper is devoted to study the warm inflation using vector fields in the background of locally rotationally symmetric Bianchi type I universe model. We formulate the field equations, slow-roll and perturbation parameters (scalar and tensor power spectra as well as their spectral indices) under slow-roll approximation. We evaluate all these parameters in terms of directional Hubble parameter during intermediate and logamediate inflationary regimes by taking the dissipation factor as a function of scalar field as well as a constant. In each case, we calculate the observational parameter of interest, i.e., tensor-scalar ratio in terms of inflation. The graphical behavior of these parameters shows that the anisotropic model is also compatible with WMAP7 and Planck observational data., Comment: 25 pages, 8 figures

In this paper, we investigate the statefinder, the deceleration and equation of state parameters when universe is composed of generalized holographic dark energy or generalized Ricci dark energy for Bianchi I universe model. These parameters are found for both interacting as well as non-interacting scenarios of generalized holographic or generalized Ricci dark energy with dark matter and generalized Chaplygin gas. We explore these parameters graphically for different situations. It is concluded that these models represent accelerated expansion of the universe., Comment: 24 pages, 19 figures

This paper is devoted to check validity of the laws of thermodynamics for LRS Bianchi type I universe model which is filled with combination of dark matter and dark energy. We take two types of dark energy models, i.e., generalized holographic dark energy and generalized Ricci dark energy. It is proved that the first and generalized second law of thermodynamics are valid on the apparent horizon for both the models. Further, we take fixed radius $L$ of the apparent horizon with original holographic or Ricci dark energy. We conclude that the first and generalized second laws of thermodynamics do not hold on the horizon of fixed radius $L$ for both the models., Comment: 12 pages, 2 figures