In this work, we apply the generalised Feshbach Villars transformation (GFVT) to spin-0 scalar fields in a Schwarzschild gravitational background. Starting from the covariant Klein Gordon equation, we reformulate the dynamics in the FV two-component representation, which enables a natural separation of positive- and negative-energy branches. In the far-field approximation, the system exhibits a hydrogen like bound spectrum, confirming the ability of GFVT to provide a consistent probabilistic interpretation in curved spacetime. We then extend the formalism by introducing a relativistic harmonic oscillator potential, which transforms the radial equation into a biconfluent Heun form. The requirement of square integrability leads to a discrete oscillator spectrum that remains independent of the gravitational parameter, with gravity appearing only through selection rules on the admissible quantum states. Explicit wave functions, probability densities, and graphical results are presented, illustrating the internal consistency of the method. Overall, this study demonstrates the effectiveness of GFVT as a bridge between relativistic quantum mechanics and curved geometry, and it highlights its potential for future applications in strong gravitational fields.

This paper investigates scalar perturbations and quasinormal modes (QNMs) associated with cylindrical black holes constructed within the frameworks of $f(\mathcal{R})$-gravity and Ricci-Inverse ($\mathcal{RI}$) gravity. Moreover, we study the modified Hawking radiation in these black hole solutions and analyze the effects of coupling constants. These modified theories, which extend general relativity by introducing higher-order curvature corrections and additional geometric terms, provide a rich platform for exploring deviations from standard gravitational physics. The study begins by revisiting the cylindrical black holes in these modified gravity theories, where the effective cosmological constants respectively, are represented by $\Lambda_m^{f(\mathcal{R})}$ and $\Lambda_m^{\mathcal{RI}}$ related to the coupling constants unique to each framework. Afterwards, the QNMs, intrinsic damped oscillations of the black hole space-time, are analyzed to probe the stability of the system, with the effective potential $V$ revealing the impact of the modified gravity parameters. Additionally, the thermodynamic properties of the black holes are examined through the lens of the Generalized Uncertainty Principle (GUP), which introduces quantum corrections to Hawking radiation. The GUP-modified Hawking temperature and entropy are derived, demonstrating significant deviations from classical results and highlighting the quantum gravitational effects in these modified frameworks. By linking QNMs, thermodynamics, and quantum corrections, this work not only deepens the understanding of modified gravity theories but also offers potential observational pathways to test their validity.

We study the relativistic quantum dynamics of spin-0 particles in the spacetime of a spinning cosmic string that carries both spacelike disclination (conical deficit $\alpha$) and screw dislocation (torsion $J_z$), as well as frame dragging ($J_t$). Using the Feshbach-Villars (FV) reformulation of the Klein-Gordon equation, we obtain a first-order Hamiltonian with a positive-definite density, enabling a clean probabilistic interpretation for bosons in curved or topologically nontrivial backgrounds. In the weak-field regime (retaining terms $\mathcal{O}(G)$ and discarding the $\mathcal{O}(G^2)$ contribution that would otherwise lead to double-confluent Heun behavior), separation of variables in a finite cylinder of radius $R_0$ yields a Bessel radial equation with an effective index $\nu(\alpha, J_t, J_z; E, k)$ that mixes rotation and torsion. The hard-wall condition $J_\nu(\kappa R_0) = 0$ quantizes the spectrum, $E_n^2 = m^2 + k^2 + \left(\frac{j_{\nu,n}}{R_0}\right)^2$. Working in the stationary positive-energy sector, we derive closed-form normalized eigenfunctions and FV density, and we evaluate information-theoretic indicators (Fisher information and Shannon entropy) directly from the FV probability density. We find that increased effective confinement (via geometry/torsion) enhances Fisher information and reduces position-space Shannon entropy, quantitatively linking defect parameters to localisation/complexity. The FV framework thus provides a robust, computationally transparent route to spectroscopy and information measures for scalar particles in rotating/torsional string backgrounds, and it smoothly reproduces the pure-rotation, pure-torsion, and flat-spacetime limits.

Medical image analysis suffers from a lack of labeled data due to several challenges including patient privacy and lack of experts. Although some AI models only perform well with large amounts of data, we will move to data augmentation where there is a solution to improve the performance of our models and increase the dataset size through traditional or advanced techniques. In this paper, we evaluate the effectiveness of data augmentation techniques on two different medical image datasets. In the first step, we applied some transformation techniques to the skin cancer dataset containing benign and malignant classes. Then, we trained the convolutional neural network (CNN) on the dataset before and after augmentation, which significantly improved test accuracy from 90.74% to 96.88% and decreased test loss from 0.7921 to 0.1468 after augmentation. In the second step, we used the Mixup technique by mixing two random images and their corresponding masks using the retina and blood vessels dataset, then we trained the U-net model and obtained the Dice coefficient which increased from 0 before augmentation to 0.4163 after augmentation. The result shows the effect of using data augmentation to increase the dataset size on the classification and segmentation performance.

Variational autoencoder (VAE) is one of the most common techniques in the field of medical image generation, where this architecture has shown advanced researchers in recent years and has developed into various architectures. VAE has advantages including improving datasets by adding samples in smaller datasets and in datasets with imbalanced classes, and this is how data augmentation works. This paper provides a comprehensive review of studies on VAE in medical imaging, with a special focus on their ability to create synthetic images close to real data so that they can be used for data augmentation. This study reviews important architectures and methods used to develop VAEs for medical images and provides a comparison with other generative models such as GANs on issues such as image quality, and low diversity of generated samples. We discuss recent developments and applications in several medical fields highlighting the ability of VAEs to improve segmentation and classification accuracy.

This research focus on the investigation of relativistic quantum dynamics of spin0 scalar particles/fields through the utilization of the Klein-Gordon (KG) equation within the framework of an electrovacuum space-time in the presence of an external scalar potential. Specifically, we focus on a cylindrical symmetric Bonnor-Melvin magnetic universe with a cosmological constant, where the magnetic field aligns along the symmetry axis direction. We derive the radial wave equation of the KG-equation by considering a Cornell-type scalar potential in the background of magnetic universe and successfully obtain an analytical eigenvalue solution for spin-0 quantum system. Notably, our findings reveal that both the energy spectrum and the corresponding radial wave function are significantly influenced by the presence of the cosmological constant, the topology parameter of the space-time geometry, which induces a deficit in the angular coordinates, and the potential parameters.

This paper investigates the energy spectrum of the Dirac oscillator within the framework of Doubly Special Relativity (DSR), focusing on two prominent models: the Magueijo--Smolin (MS) and Amelino-Camelia models. We derive the modified Dirac equations in both MS and Amelino-Camelia DSR models under the approximation of $$O(E^{2}/k^{2})$$ for a single particle and examine the resulting energy spectra. The study reveals significant corrections to the standard relativistic Dirac oscillator spectrum due to the Planck-scale deformation parameter $$k$$, which introduces distinct deviations depending on the DSR model employed. For the MS model, we observe non-uniform shifts in both positive and negative energy branches at small $$k$$, with the spectrum gradually flattening toward the canonical result as $$k$$ increases. In the Amelino-Camelia model, the energy levels show larger deviations at lower values of $$k$$, and these anomalies diminish more slowly compared to the MS model. The results provide insights into the impact of quantum gravity effects on quantum systems, with potential applications in high-precision spectroscopic or astrophysical observations at energies near the Planck scale. Furthermore, the comparative analysis of these two DSR models highlights the robustness of Planck-scale predictions and guides future experimental efforts aimed at detecting quantum-gravity signatures.

In this article, we investigate asymptotically flat non-exotic traversable wormhole geometries within the King and Dekel-Zhao dark matter halos in the framework of $f(R, L_m)$ gravity. Two functional forms of the theory are considered: Model-I: $f(R, L_m)=(R/2) + L_m^{\alpha}$ and Model-II: $f(R, L_m)=(R/2) + (1 + \lambda R)L_m$. For both models, wormhole solutions are obtained and analyzed using the King and Dekel-Zhao dark matter density profiles, allowing us to explore how the underlying matter distribution influences the wormhole structures. The energy conditions are examined to verify the feasibility of sustaining the wormhole geometries with non-exotic matter, while embedding surfaces, proper radial distance, and total gravitational energy are studied to illustrate the wormhole's physical viability and traversability. Moreover, we test the strong deflection angle and its implications for gravitational lensing and show possible observational signatures of such wormhole configurations. Our results indicate that within $f(R, L_m)$ gravity, and for appropriate parameter choices, dark matter environments can sustain physically consistent non-exotic traversable wormhole geometries with distinct gravitational lensing signatures, providing new insights into the interplay between modified gravity, dark matter, and astrophysical observations.

This paper investigates the scattering states of spin-1/2 particles in the spacetime of a spinning cosmic string with spacelike disclination and dislocation, with and without a Coulomb interaction. Working within the tetrad formalism, we solve the Dirac equation for several configurations of the angular momentum density $J_t$ and the torsion parameter $J_z$ that are relevant from a physical perspective. These configurations include balanced torsion ($J_t = J_z$), pure spinning strings ($J_z = 0$), pure screw dislocations ($J_t = 0$) and the general case. In all cases, the geometry modifies an effective azimuthal quantum number, and for strong rotation it introduces a geometric radial cutoff $\rho_c$ that acts as a hard wall. These factors lead to closed-form expressions for the radial wave functions, phase shifts and differential cross sections, which are expressed in terms of confluent hypergeometric and Bessel functions. We demonstrate that conical curvature, rotation and torsion generate Aharonov-Bohm-like contributions, as well as energy- and momentum-dependent asymmetries in Dirac-Coulomb scattering. This results in topology-renormalised Mott/Rutherford patterns. In the Coulomb-free limit, scattering becomes purely geometric yet still exhibits characteristic forward enhancement, which is governed by defect parameters and the cutoff. We briefly discuss possible realisations in Dirac materials, such as strained or defective graphene, where lattice disclinations and dislocations mimic the cosmic-string geometry.

In this analysis, we study the dynamics of quantum oscillator fields within the context of a position-dependent mass (PDM) system situated in an Einstein-Maxwell space-time, incorporating a non-zero cosmological constant. The magnetic field is aligned along the symmetry axis direction. To analyze PDM quantum oscillator fields, we introduce a modification to the Klein-Gordon equation by substituting the four-momentum vector $p_{\mu} \to \Big(p_{\mu}+i\,\eta\,X_{\mu}+i\,\mathcal{F}_{\mu}\Big)$ into the Klein-Gordon equation, where the four-vector is defibed by $X_{\mu}=(0, r, 0, 0)$, $\mathcal{F}_{\mu}=(0, \mathcal{F}_r, 0, 0)$ with $\mathcal{F}_r=\frac{f'(r)}{4\,f(r)}$, and $\eta$ is the mass oscillator frequency. The radial wave equation for the relativistic modified Klein-Gordon equation is derived and subsequently solved for two distinct cases: (i) $f(r)=e^{\frac{1}{2}\,\alpha\,r^2}$, and (ii) $f(r)=r^{\beta}$, where $\alpha \geq 0, \beta \geq 0$. The resultant energy levels and wave functions for quantum oscillator fields are demonstrated to be influenced by both the cosmological constant and the geometrical topology parameter which breaks the degeneracy of the energy spectrum. Furthermore, we observed noteworthy modifications in the energy levels and wave functions when compared to the results derived in the flat space background.

This study employs the Riesz-Feller fractional derivative to determine Fisher and Shannon parameters for a one-dimensional harmonic oscillator. By deriving the Riesz fractional derivative of the probability density function, we quantify both Fisher information and Shannon entropy, thus providing valuable insights into the system's probabilistic nature.

We investigate the geometric and physical properties of an anti-de Sitter (AdS) black hole space-time coupled by a cloud of strings and surrounded by a quintessence-like fluid, all within the framework of non-commutative (NC) geometry. From the perspective of geometrical optics, we analyze the behavior of null geodesics, focusing on key optical features such as the effective potential, the structure and radius of the photon sphere, light deflection angles, photon trajectories, and the resulting black hole (BH) shadow. Our findings show that the combined effects of the string cloud and quintessence-like fluid significantly modify photon dynamics and optical observables, leading to notable deviations from standard BH scenarios in NC geometry background. We also examine time-like geodesics, with particular emphasis on the innermost stable circular orbits (ISCOs). The results demonstrate that the presence of geometric matter components alters the ISCO radius compared to conventional solutions. In addition, we explore the thermodynamic behavior of the BH, deriving expressions for the Hawking temperature, entropy, Gibbs free energy, and specific heat capacity. The influence of the string cloud and quintessence-like fluid introduces substantial modifications to the thermodynamic profile, including shifts in phase transition points and changes to stability conditions under NC geometric effects. Furthermore, we study the dynamics of massless scalar field perturbations in this modified background by formulating the Klein-Gordon equation and reducing it to a Schrödinger-like form via separation of variables. The resulting effective potential is analyzed in detail, highlighting the significant role of both the string cloud and the quintessence-like fluid in shaping the perturbative landscape within the NC geometry setting.

Inspired by Loop Quantum Gravity (LQG), we investigate the Reissner-Nordström (RN) black hole (BH) solution coupled with a cloud of strings in an anti-de Sitter (AdS) background, surrounded by a quintessence-like fluid. We begin by analyzing the optical properties of the BH through null geodesic motion, deriving an effective potential that governs photon dynamics. This effective potential is central to understanding key phenomena such as photon trajectories, circular null orbits, photon sphere, and the resulting BH shadow. Subsequently, we study the dynamics of neutral test particles by deriving effective potential that describes their motion. Using the potential, we compute the specific energy and specific angular momentum of neutral particles in circular orbits around the BH and analyze the outcomes. We also investigate the innermost stable circular orbits (ISCO) and demonstrate how various geometrical and physical properties influence the radius of ISCO. Furthermore, we explore the thermodynamic properties of the BH solution by deriving key quantities such as the Hawking temperature, entropy, Gibbs free energy, internal energy, and specific heat capacity. Throughout the study, we demonstrate that the geodesic structure, scalar field behavior, and thermodynamic properties are significantly influenced by parameters such as the string cloud, quantum correction, electric charge, the surrounding quintessence-like fluid, and the AdS curvature radius.

In this study, we explore the thermodynamic properties of a Schwarzschild black hole (BH) embedded in an anti-de Sitter (AdS) background, which is further coupled with a cloud of strings and surrounded by a quintessence-like fluid. Beginning with the formulation of BH mass in terms of the event horizon radius, we incorporate the concept of pressure as related to the AdS curvature radius within the framework of extended phase space thermodynamics. Using this setup, we derive key thermodynamic quantities, including the Gibbs free energy and internal energy, to characterize the energetic behavior of the black hole system. To assess the stability of the black hole, we compute the specific heat capacity and analyze how it is influenced by external parameters, such as the string cloud and the quintessence-like fluid. These geometric and matter fields are shown to significantly modify the thermal response of the BH. Furthermore, we examine the inversion temperature associated with the black hole and highlight its distinction from the standard Hawking temperature, providing deeper insight into the phase structure. Additionally, we investigate the Joule-Thomson expansion process and demonstrate how the aforementioned parameters affect this thermodynamic phenomenon, showing important aspects of BH cooling and heating behavior in an extended thermodynamic context.

The Einstein-Cartan (EC) theory of gravity provides a natural extension of general relativity by incorporating spacetime torsion to account for the intrinsic spin of matter. In this work, we investigate Yukawa-Casimir traversable wormholes supported by three distinct Yukawa-Casimir energy density profiles within the framework of EC gravity. The resulting shape functions are shown to satisfy all the fundamental requirements for traversable wormhole geometries. Our analysis reveals that the presence of exotic matter is unavoidable in sustaining these wormholes, and we quantify its total amount through the volume integral quantifier. Furthermore, the equilibrium of the wormhole configurations is established by examining the Tolman-Oppenheimer-Volkoff equation. To enhance the physical relevance of the present work, we study several key features of the wormholes, including the embedding surface, proper radial distance, tidal forces, and total gravitational energy. In addition, we analyze the optical properties of wormholes by examining both the shadow and the strong deflection angle. All the findings collectively demonstrate the physical plausibility of Yukawa-Casimir traversable wormholes within the EC gravity framework.

In this work, we tested the physical properties of Rastall black holes in the presence of string clouds and quintessence. The modified spacetime geometry arising from the Rastall framework is first established, providing the basis for analyzing the geodesic structure. We study null geodesics in detail, testing photon trajectories, the conditions for photon spheres, BH shadows, the associated effective radial force, and the topological features of photon rings. Also, the analysis is further tested to timelike geodesics, where we investigate the motion of massive particles and determine the innermost stable circular orbits. In this case, we discuss the thermodynamic behavior of the system, show the effects of Rastall gravity, strings, and quintessence on the BHs stability and thermal characteristics. In this context, our results improve and show of how modifications to general relativity and surrounding matter distributions influence both the dynamical and thermodynamical aspects of BHs.

We study the Dirac oscillator for spin-1/2 particles in a spacetime containing a spinning cosmic string endowed with both curvature (disclination) and torsion (screw dislocation). The background geometry includes off-diagonal and is analyzed through a local tetrad formalism. Working in cylindrical coordinates, we derive the covariant Dirac equation and solve it exactly via a second-order differential equation for the lower spinor component. Three distinct physical configurations are examined: (i) balanced torsion where temporal and spatial contributions are equal, (ii) purely temporal torsion (spinning string), and (iii) purely spatial torsion (screw dislocation). In all cases, we obtain exact energy spectra expressed in terms of effective angular quantum numbers that depend on the oscillator frequency, the angular deficit parameter \alpha , the torsional parameters J_{t} and J_{z}, and the longitudinal momentum k. The resulting energy levels generalize the flat-spacetime Moshinsky oscillator spectrum by incorporating energy- and momentum-dependent shifts due to the background geometry. We show that curvature and torsion lift degeneracies and induce nontrivial modifications to the angular structure of the solutions. The flat-space spectrum is recovered as a special limit when both curvature and torsion vanish. This work provides a fully solvable model that illustrates how spacetime defects affect relativistic quantum systems, offering insights relevant to both high-energy physics and condensed-matter analogs.

We investigate the geometric and physical properties of an anti-de Sitter (AdS) black hole space-time coupled by a cloud of strings and surrounded by a quintessence-like fluid, all within the framework of non-commutative (NC) geometry. From the perspective of geometrical optics, we analyze the behavior of null geodesics, focusing on key optical features such as the effective potential, the structure and radius of the photon sphere, light deflection angles, photon trajectories, and the resulting black hole (BH) shadow. Our findings show that the combined effects of the string cloud and quintessence-like fluid significantly modify photon dynamics and optical observables, leading to notable deviations from standard BH scenarios in NC geometry background. We also examine time-like geodesics, with particular emphasis on the innermost stable circular orbits (ISCOs). The results demonstrate that the presence of geometric matter components alters the ISCO radius compared to conventional solutions. In addition, we explore the thermodynamic behavior of the BH, deriving expressions for the Hawking temperature, entropy, Gibbs free energy, and specific heat capacity. The influence of the string cloud and quintessence-like fluid introduces substantial modifications to the thermodynamic profile, including shifts in phase transition points and changes to stability conditions under NC geometric effects. Furthermore, we study the dynamics of massless scalar field perturbations in this modified background by formulating the Klein-Gordon equation and reducing it to a Schrödinger-like form via separation of variables. The resulting effective potential is analyzed in detail, highlighting the significant role of both the string cloud and the quintessence-like fluid in shaping the perturbative landscape within the NC geometry setting.

The Einstein-Cartan (EC) theory of gravity provides a natural extension of general relativity by incorporating spacetime torsion to account for the intrinsic spin of matter. In this work, we investigate Yukawa-Casimir traversable wormholes supported by three distinct Yukawa-Casimir energy density profiles within the framework of EC gravity. The resulting shape functions are shown to satisfy all the fundamental requirements for traversable wormhole geometries. Our analysis reveals that the presence of exotic matter is unavoidable in sustaining these wormholes, and we quantify its total amount through the volume integral quantifier. Furthermore, the equilibrium of the wormhole configurations is established by examining the Tolman-Oppenheimer-Volkoff equation. To enhance the physical relevance of the present work, we study several key features of the wormholes, including the embedding surface, proper radial distance, tidal forces, and total gravitational energy. In addition, we analyze the optical properties of wormholes by examining both the shadow and the strong deflection angle. All the findings collectively demonstrate the physical plausibility of Yukawa-Casimir traversable wormholes within the EC gravity framework.

This research paper delves into the study of a non-relativistic quantum system, considering the interplay of non-inertial effects induced by a rotating frame and confinement by the Aharonov-Bohm (AB) flux field with potential in the backdrop of topological defects, specifically a screw dislocation. We first focus on the harmonic oscillator problem, incorporating an inverse-square repulsive potential. Notably, it becomes evident that the energy eigenvalues and wave functions are intricately influenced by multiple factors: the topological defect parameter $\beta$ (representing the screw dislocation), the presence of a rotating frame engaged in constant angular motion with speed $\Omega$, and the external potential. Then we study the quantum behavior of non-relativistic particles, engaging in interactions governed by an inverse square potential, all while taking into account the effects of the rotating frame. In both scenarios, a significant observation is made: the quantum flux field's existence brings about a shift in the energy spectrum. This phenomenon bears a resemblance to the electromagnetic Aharonov-Bohm effect.