This article analyzes the anisotropic charged solutions for compact stars within the framework of extended symmetric teleparallel gravity, wherein anisotropy has been generated in compact stars via gravitational decoupling. The renowned Tolman-Finch-Skea solution and Buchdahl metric are utilized to derive two sets of solutions for a pure extended symmetric teleparallel gravity, specifically within the context of pure f(Q,T) gravity. Meanwhile, the decoupled system is addressed using the Einasto spike dark matter density profile, which introduces anisotropy into the system. We evaluate the viability of modeling charge-dark matter compact stars with the Einasto spike density profile. Within this paradigm, we delineate the temporal aspect of the Theta 00-field sector to accurately quantify the impact of dark matter on the gravitational matter source. An detailed graphical examination of the structural factors and stability demonstrates that both models, given the selected parameters, yield well-behaved and physically consistent results. The findings of this investigation are both feasible and commendable, offering significant insights. The equilibrium of forces, derived from the modified TOV equations, illustrates a stable balance among gravitational, electrostatic, and hydrostatic factors. The analysis encompassed the modeling of three distinct stellar candidates, incorporating their mass-radius relation constraints for GW190814 (2.5-2.67), PSR J2215 + 5135 (2.28+0.10-0.09), and PSR J1810 + 1744 (2.13 +/- 0.04).-utilizing observable astrophysical data, the corresponding radii were determined to fall within the range [9.7, 12.58] km. The mass-radius relationship indicates a maximum mass, with associated radii closely aligning with observational limits.

In this paper, we explore traversable wormhole geometries exhibiting static and spherical symmetry in the context of torsion-based teleparallel theory, specifically the f(& Tscr; ) theory where & Tscr; denotes the torsion scalar. The wormhole shape function is exactly derived using a Dymnikova-Schwinger density profile with generalized uncertainty principle corrections, followed by an analysis of the geometric conditions for physical validity, while three rotation curve models are used to construct the redshift functions. To construct the redshift functions, we consider three different galactic rotation curve profiles, leading to three distinct wormhole solutions (Solution-I, Solution-II, and Solution-III). Our findings indicate that the wormhole solutions satisfy essential geometric requirements such as the throat condition, flaring-out behavior, and asymptotic flatness. Nevertheless, the null energy condition is violated close to the throat, pointing to the presence of exotic matter. A comparative analysis reveals that the three rotation curve-inspired redshift functions lead to different thermodynamic stability behaviors. Our findings show thermal stability, with specific heat revealing stable regions along the radial coordinate (1.5, 6], (1.5, 2], and (1.5, 11.8] for Solution-I, Solution-II, and Solution-III, respectively. Our findings confirm that the model is both physically viable and stable.

In the world economy, silver has dual uses: it is not only an asset for investment but is used as a precious metal in industry. The use of silver will become even more strategic as the transition to new energy technologies - including photovoltaics, batteries and electric vehicles - begins. This study looks at how global volatility effects the price dynamics of silver from January 2005 through December 2024. Various test methodologies were used: the ADF/KPSS stationarity tests, GARCH (1,1)/EGARCH volatility model, Johansen cointegration, VAR/VECM framework and, finally, the Diebold/Yilmaz (2012) spill-over index to measure the size and direction of spill-over effects between assets, as well as impulse response functions to illustrate how silver reacts to macroeconomic shocks. The findings show that there are some strong resistance and clustering in the silver market (α + β ≈ 0.95). We find a good relationship between the silver price and the VIX; this indicates that the demand for silver tends to increase when market uncertainty causes a flight to safety, and silver appears to act as a hedge against inflation. The Total Spillover Index for silver was found to be 5.51%, which shows that silver represents a significant contributor to the transfer of volatility across the larger financial system; Johansen's cointegration analysis suggests that a long-run relationship exists between silver and other assets, and the VECM's error correction term of -0.142 (p < 0.01) shows an average monthly adjustment rate to reach the long-run equilibrium of around 14.2%. Overall, these results provide new evidence to the literature regarding the relationship between precious metals and financial volatility and provide insights into how to build a portfolio, the regulation of commodity derivatives, and the management of risk associated with industrial production/consumption in an increasingly financialized and sustainable global economy.

This paper investigates light deflection in wormhole spacetimes within the extended gravity model f ( R , L m ) = α ( R + β α L m ) $f(\mathcal {R}, \mathcal {L}_m)=\alpha \nobreakspace (\mathcal {R}+\frac{\beta }{\alpha }\nobreakspace \mathcal {L}_m)$ , where R $\mathcal {R}$ and L m $\mathcal {L}_m$ are Ricci scalar and Lagrangian matter, respectively. Inspired by the density formulations proposed by Elizalde and Khurshudyan  [ https://doi:10.1103/PhysRevD.99.024051 Phys. Rev. D 99 , no.2, 024051 (2019)], the profiles ρ ( R , R ′ ) = λ 1 R + λ 2 R ′ $\rho (\mathcal {R}, \mathcal {R}^\prime)=\lambda _{1}\nobreakspace \mathcal {R}+\lambda _{2}\nobreakspace \mathcal {R}^\prime$ and ρ ( R 2 , R ′ ) = λ 1 R 2 + λ 2 R ′ $\rho (\mathcal {R}^2, \mathcal {R}^\prime)=\lambda _{1}\nobreakspace \mathcal {R}^2+\lambda _{2}\nobreakspace \mathcal {R}^\prime$ are used to derive shape functions that meet the necessary conditions for wormhole traversability. The Tolman–Oppenheimer–Volkoff (TOV) equation maintains equilibrium through the hydrostatic and anisotropic balancing forces. The deflection angle highlights lensing transitions, the volume integral quantifier indicates minimal exotic matter, and the growth of the effective potential with angular momentum signals orbit stability. The linear perturbation approach identifies the stability region, demonstrating that the adopted configurations produce stable, traversable wormholes with realistic lensing.

Within the framework of asymptotically safe gravity, we investigate traversable wormhole configurations sourced by dark matter halos modeled through the Burkert density profile. In this setting, the wormhole shape function is determined by the interplay between the adopted mass-density distribution and the modified gravitational field equations. The analysis proceeds by employing the tangential velocity profile to infer the redshift function. A scale-dependent gravitational coupling, c(k), obtained from the infrared renormalization group flow of asymptotically safe gravity, is incorporated into the field equations to consistently include quantum gravitational corrections at astrophysical length scales. We analyze the standard energy conditions and demonstrate that the null energy condition is violated in the neighborhood of the wormhole throat, in agreement with the generic behavior of traversable wormhole spacetimes. Furthermore, we construct embedding diagrams to visualize the spatial geometry and to elucidate the flaring-out condition at the throat.

In this work, Static wormhole models are examined within the framework of curvature-based f(R,Lm,T) gravity theory. A relationship between the matter energy density and pressure is proposed for the Morris-Thorne wormhole geometry with a constant redshift function. By incorporating a gradient-dependent equation of state (Pr=Pr(ρ,ρ′) and Pt=Pt(Pr,Pr′)), we derive exact wormhole solutions for two representative cases. Our analysis shows that exact wormhole models can admit null energy condition violations localized at the throat, while preserving a non-negative matter energy density. The stability analysis is performed via the Tolman–Oppenheimer-Volkoff equation under hydrostatic equilibrium, demonstrating that the balance among anisotropic and hydrostatic forces sustains the wormhole’s stable configuration. For positive and negative values of ζ, the energy flux attains a pronounced negative magnitude, inducing an outward flux that supports the stability of the wormhole throat. The geometric characteristics of the wormhole are examined through embedding diagrams, and the total exotic matter required to maintain the configuration is evaluated using the volume integral quantifier. Simultaneously, the effective potential demonstrates enhanced photon confinement and increased stability of particle orbits.

This study examines the propagation of photons around slowly rotating wormholes supported by the fuzzy dark matter density profile within the framework of asymptotically safe gravity. The resulting wormhole geometry is characterized by a shape function that arises from the interplay between the specified energy density profile and the modified field equations within a Teo-type rotating wormhole metric. We examine the role of quantum-corrected redshift profiles and rotation in determining photon-sphere locations. To investigate the influence of varying redshift behaviors, we employ three smooth functions-Modified Bessel, Logarithmic nonlocal, and Error function nonlocal to analyze their impact on photon motion, null geodesics, effective potentials, photon-sphere radii, and the Lense-Thirring precession induced by wormhole rotation. This framework enables a detailed analysis of the wormhole geometry, including the throat configuration, the flaring-out condition necessary for traversability, and the violation of the null energy condition.

This paper provides a comprehensive comparative analysis of wormhole solutions governed by four distinct dark energy configurations within the context of f(R,L-m,T ) gravity. Every dark energy profile has a distinct form function that fulfills the geometric criteria required for a traversable wormhole. By adjusting the dark energy parameter eta within a limited range (0 <= eta <= 0.002), we specify the range where the null energy requirement is breached, hence facilitating wormhole formation. The structure of the wormhole, especially its flare-out geometry, is shown by embedding diagrams. Our analysis of the deflection angle reveals an inward bending of light beyond a certain radial distance, and the existence of positive total gravitational energy in all models corroborates their physical plausibility. An exoticity study has been conducted for each model structure. This thorough study offers novel insights into the gravitational effects of holographic dark energy in enabling stable wormhole formations.

This paper investigates light deflection in wormhole spacetimes within the extended gravity model , where and are Ricci scalar and Lagrangian matter, respectively. Inspired by the density formulations proposed by Elizalde and Khurshudyan [ Phys. Rev. D 99, no.2, 024051 (2019)], the profiles and are used to derive shape functions that meet the necessary conditions for wormhole traversability. The Tolman-Oppenheimer-Volkoff (TOV) equation maintains equilibrium through the hydrostatic and anisotropic balancing forces. The deflection angle highlights lensing transitions, the volume integral quantifier indicates minimal exotic matter, and the growth of the effective potential with angular momentum signals orbit stability. The linear perturbation approach identifies the stability region, demonstrating that the adopted configurations produce stable, traversable wormholes with realistic lensing.

In this study, asymptotically flat wormholes are modeled within the framework of Rastall gravity using a gradient-dependent equation of state expressed as Pr=Pr(ρ,ρ′). This formulation incorporates both the energy density and its radial gradient into the radial pressure, allowing us to derive the corresponding shape functions for the first time and examine their physical characteristics. The wormhole configurations obtained are found to be viable for negative values of the Rastall parameter λ. The parameters λ, α, and β play a crucial role in determining the stability of these solutions. As α and λ take more negative values and β increases, the energy flux acquires a stronger negative magnitude, producing an outward flow that stabilizes the throat region. Similarly, the behavior of the effective potential shows enhanced photon confinement and improved orbital stability under the same parameter variations. Together, these trends confirm the physical consistency and dynamical viability of wormhole geometries supported by the gradient-driven equation of state in Rastall gravity.

Abstract This article explores traversable wormhole geometries obtained in the context of the symmetric teleparallel gravity theory and highlights their distinctive physical characteristics. Our methodology involves determining the tidal force by employing a specified form of the shape function along with an appropriate equation of state for Case I. In order to extract the shape functions associated with the wormhole solution, we apply the null-complexity condition with tidal force in Case II. In Case III, we utilize the balancing Tolman–Oppenheimer–Volkoff equation in conjunction with a tidal force to obtain viable wormhole shape function. The analysis focuses on the dependence of wormhole characteristics on the parameter $$\zeta $$ ζ . The energy conditions are examined within their respective validity domains for various ranges of the model parameters. We also calculate, the volume integral quantifier, the extent of exotic matter needed to uphold the traversable wormhole structure. Through the effective potential for timelike geodesics, the influence of angular momentum on trajectories is clarified, and the corresponding deflection angle evaluation points to significant light bending close to the throat. By introducing small radial perturbations around the equilibrium shell radius, we examine the stability characteristics for all considered shape functions.

In this work, we investigate traversable wormhole solutions in the context of modified curvature matter coupling gravity described by the $f(\mathcal{R}, \mathcal{L}_{matter}, \mathcal{T})$ framework. The study focuses on static wormhole configurations, assuming a constant redshift function. We consider a linear form of the gravitational action and systematically investigate the impact of varying one of its coupling constants on the wormhole geometry. This work investigates traversable wormhole solutions in the presence of various dark matter density distributions, specifically Moore, Thomas Fermi, and Einasto profiles. An analysis of the relevant physical quantities reveals that the wormhole configurations associated with different dark matter profiles violate the NEC, indicating that dark matter plays a crucial role in sustaining traversable wormholes in galactic halo environments, while equilibrium is achieved for specific ranges of the free parameters. Moreover, the wormhole configurations are characterized using the volume integral quantifier, deflection angle of light, and embedding diagram. These findings suggest that wormhole solutions supported by various dark matter profiles within the $f(\mathcal{R}, \mathcal{L}_{matter}, \mathcal{T})$ gravity framework are physically feasible and consistent.

This study examines the spatio-temporal evolution of industries along the NH-48 corridor. It focuses on a 127-kilometre stretch from Gurugram to Behror in India’s National Capital Region. The research employs exponential growth modelling and distance-decay analysis to assess the relationship between industrial concentration and highway proximity across four policy phases (pre-1991, 1991–2001, 2001–2011 and 2011–2025). Secondary data about industries, population and location are utilised for the study. The findings reveal a pronounced clustering of large-scale industries within 3 km of the highway and an exponentially declining industrial density beyond this distance. Medium-scale industries exhibit a broader distribution extending up to 7 km, indicating greater diffusion and linkage-driven expansion. A strong negative correlation is observed between industrial density and distance from NH-48. Large-scale industries show a higher decay coefficient (b = 1.57) than medium-scale industries (b = 0.68). Annual growth rates indicate spatial maturation and southward diffusion of the corridor. The results reveal that industrial clustering is driven by infrastructure accessibility and the study emphasises the need for a more balanced and multi-nodal industrial policy.

This paper aims to investigate the possibility of generating exact solutions for appropriate anisotropic spherically symmetric systems in F(Q,T) gravity where Q and T are non-metricity and the trace of the energy-momentum tensor respectively. These solutions involve embedding a spherically symmetric static metric into a five-dimensional pseudo-Euclidean space. To solve Einstein's field equations and ensure that the solution is free of center singularities, a physically plausible selection of the metric coefficient grr is used. With the help of the Karmarkar condition, we compute the gtt component of the metric tensor using the metric coefficient grr. At the boundary of the compact star, we match interior spacetime with the exterior spacetime to find the values of unknown constants. To make the solution match the measured mass and radius, we have tuned up the solution for compact star PSRJ1614-220. The behavior of the solution has been thoroughly examined for the same star. By examining the necessary physical characteristics, such as energy conditions, causality condition, hydrostatic equilibrium, pressure-density ratio, Herera Cracking criterion, etc., the physical acceptability of the model in the context of F(Q,T) has been investigated. It is observed that the present solution allows viable modeling of stellar objects in F(Q,T) gravity.

This study explores static, spherically symmetric wormhole solutions within the framework of massive gravity (dRGT) de Rham-Gabadadze-Tolley (dRGT) for the first time, incorporating mixed-energy density and holographic dark energy (DE) density profiles using the Minimal Geometric Deformation (MGD) method proposed by Ovalle (2017). Using unique density profiles, the corresponding shape functions are calculated. The key characteristics of wormholes, including flaring-out condition and asymptotical flatness, are examined in depth. Through the MGD approach, this study constructs wormhole solutions, with the decoupling parameter gamma serving as a key factor influencing their geometry and energy constraints. The embedded diagrams illustrate the upper and lower universes, which are influenced by the effects of newly determined shape functions. In addition, the volume integral quantifier (VZQ) is evaluated, shedding light on the exotic matter required near the wormhole throat. The stability of the wormhole solution is confirmed by satisfying equilibrium criteria through the balancing of different forces. Both models suggest that real-world wormhole solutions are feasible due to the increasing active gravitational mass (Ac.M). Through a detailed analysis of shape functions, the study addresses how thin-shell wormhole stability is influenced by mass, geometric structure, and decoupling parameter, offering practical insights into constructing stable configurations in theoretical models.

In this work, we investigate the existence, stability and physical viability of wormhole solutions within the framework of T(Q) gravity, a modified gravity theory where Q represents the nonmetricity scalar. In this study, we developed wormhole models using holographic dark energy density profiles described by Bekenstein-Hawking and Moradpour, represented as rho bh(r) = Psi 1 pi r2 and rho m=4 pi r2(pi lambda r2+1), respectively. The derived solutions for the wormhole's shape function fulfil Psi 1 the necessary conditions. This study examines the influence of the parameters Psi 1 and Psi 2 on the equilibrium state of the wormhole solution and the breaking of energy conditions. Our findings indicate that each model deviates from the null energy condition, indicating the necessity of exotic matter for the stability of wormholes. Additionally, we analysed the geometry of wormhole models by embedding diagrams. To achieve the physical viability of the wormhole, we examined the active gravitational mass (Mactive) for both models.

This study explores the characteristics of wormhole geometries within the framework of symmetric teleparallel gravity, specifically $$\mathcal {F}(\mathcal {Q})$$ F ( Q ) gravity. By integrating holographic and mixed dark energy density profiles, we derive exact solutions for wormholes. The analysis focuses on the geometrical aspects of these wormholes, employing rotational velocity to formulate the redshift function and using dark energy density profiles to establish the shape function. By selecting specific parameter values, we show that the derived wormhole solutions meet the flare-out condition within an asymptotic background. We also evaluate the energy conditions, with particular emphasis on the null energy condition at the wormhole throat. Our findings indicate that the coupling constant $$\gamma $$ γ significantly influences the violation of energy conditions, especially the null energy condition, accompanied by graphical representations. Additionally, the research examines key features of the wormholes, such as complexity factor, anisotropy, exoticity, and embedding diagrams.

The main aim of this study is to examine the behaviour of physical parameters of an anisotropic compact star model demonstrating spherical symmetry in F(Q) modified gravity. To evaluate the behaviour and the stability of an anisotropic compact star model, we utilise the measured mass and radius of an anisotropic compact star model. This study obtained an anisotropic compact star model by solving Einstein field equations. The field equations have been simplified by an appropriate selection of the metric elements and the Karmarkar condition. By solving the field equation to develop a differential equation that establishes a relationship between two essential components of spacetime. A physical analysis of this model reveals that the resulting stellar structure for anisotropic matter distribution is a physically plausible representation of a compact star with an energy density of order $10^14 g/cm^3$. Using the Tolman-Oppenheimer-Volkoff equation, causality condition and Harrison-Zeldovich-Novikov Condition, we investigate the hydrostatic equilibrium and stability of the compact star Cen X-3. We further determined the mass-radius relation of this compact star for different values of delta}1.

In this study, our aim is to generate the new anisotropic solution for compact stellar configurations with the help of Buchdahl geometry. We used the Buchdahl metric potential [J. Astrophys. Astron. 3, 325 (1982)] to deal with the field equations in general relativity framework. To get the constant parameters, the exterior Schwarzschild de Sitter solution is linked to the interior solution at the boundary. We discuss the behavior of density, radial and tangential pressure for the present model. We take the star candidates 4U 1820-30, PSR J1903+327, 4U 1608-52, 4U 1538-52 and HerX-1 to complete our analysis. The proposed compact stars equilibrium and stability states are analyzed using the Tolman-Oppenheimer-Volkoff equation, causality condition, adiabatic index and Harrison-Zeldovich-Novikov Criterion, respectively. It is noticed that our proposed model is suitable and provides viable results with Buchdahl geometry.

In this work, we investigate an anisotropic compact star's physical properties and stability in F ( Q ) gravity. The study focuses on the significance of F ( Q ) gravity on the structure and stability of compact star, considering non-perfect fluid. Buchdahl ansatz along with transformation used to solve the Einstein field equations. We investigate the physical parameters of the 4U1820-30 compact star using a static spherical metric in the interior region and a Schwarzschild (anti) de-sitter metric in the exterior region. We investigate the behaviour of energy density(rho), radial pressure(pr), tangential pressure(pt), anisotropy(A), metric potentials, energy state parameter and energy requirements in the interior of the proposed stellar object. The equilibrium state of this star is analysed using the Tolman-Oppenheimer-Volkoff(TOV) equation and their stability is determined using the Necessary and physical existence requirements , causality condition, Harrison-Zeldovich-Novikov condition, the adiabatic index(F) method and Herrera cracking method.