Narrow Results

The main objective of this study is to investigate the stability and viability of anisotropic compact stellar objects using the Krori–Burua solutions in $f({𝒬})$ gravity, where ${𝒬}$ is a nonmetricity scalar that explains the gravitational effects. We use a static spherical metric in the inner region and Schwarzschild spacetime in the outer region of the Her X-I, SAX J 1808.4-3658 and 4U1820-30 compact stars to investigate their physical properties. By using observed values of the radius and mass of the considered compact stars, the unknown parameters are determined. We use a particular model of this theory to examine the behavior of energy density, pressure components, anisotropy, equation of state parameters and energy constraints in the interior of the proposed stellar objects. The Tolman–Oppenheimer–Volkoff equation is used to analyze the equilibrium state of these stars and causality condition, Herrera cracking method, adiabatic index methods are used to determine their stability. It is found that revolutionary technique sheds new light on the development of observationally accurate gravity model.

We consider the definition of complexity for dynamical spherically self-gravitating matter distribution in the presence of heat dissipation introduced by Herrera [L. Herrera, A. Di Prisco and J. Ospino, Phys. Rev. D 98 (2018) 104059] and generalize it in $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ gravity, where $R$ and $T$ are the Ricci scalar and the trace of energy–momentum tensor, respectively. We measure the complexity of structure as well as pattern of evolution of the fluid distribution and examine these under the effects of dark source terms of modified gravity. Some dynamical and kinematical equations are observed in the dissipative and nondissipative cases in the background of modified theory. Finally, we discuss evolution of the structure scalars and stability of a condition where the complexity factor vanishes.

In this paper, we develop a complexity factor for static sphere in modified Gauss–Bonnet gravity with anisotropic and nonhomogeneous configuration. We use the field equations as well as equation of continuity to derive expressions for mass function in $f({𝒢})$ gravity. The Riemann tensor is split using Bel’s approach to formulate structure scalars that exhibit fundamental properties of the system. A complexity factor is developed on the basis of these scalars and the condition of vanishing complexity is used to obtain solutions of two different models. It is observed that modified terms increase complexity of the matter distribution.

We have performed ab initio investigation of some physical properties of the perovskite TlMnX₃ (X = F, Cl) compounds using the full-potential linearized augmented plane wave (FP-LAPW) method. The generalized gradient approximation (GGA) is employed as exchange-correlation potential. The calculated lattice constant and bulk modulus agree with previous studies. Both compounds are found to be elastically stable. TlMnF₃ and TlMnCl₃ are classified as anisotropic and ductile compounds. The calculations of the band structure of the studied compounds showed the semiconductor behavior with the indirect (M–X) energy gap. Both compounds are classified as a ferromagnetic due to the integer value of the total magnetic moment of the compounds. The different optical spectra are calculated from the real and the imaginary parts of the dielectric function and connected to the electronic structure of the compounds. The static refractive index $n(0)$ is inversely proportional to the energy bandgap of the two compounds. Beneficial optics technology applications are predicted based on the optical spectra.

The aim of this paper is to study the charged anisotropic strange stars in the Rastall framework. Basic formulation of field equations in this framework is presented in the presence of charged anisotropic source. To obtain the solutions of the Rastall field equations in spherically symmetric Karori and Barua (KB) type space-time, we have considered a linear equation of state of strange matter, using the MIT bag model. The constraints on the Rastall dimensionless parameter $\gamma$ are also discussed to obtain the physically reasonable solution. We explore some physical features of the presented model like energy conditions, stability and hydrostatic equilibrium, which are necessary to check the physical viability of the model. We also sought for the influence of the Rastall dimensionless parameter on the behavior of the physical features of obtained solution. We plot the graphs of matter variables for different chosen values of the parameter $\gamma$ to inspect more details of analytical investigations and predict the numerical values of these variables exhibited in the tabular form. For this analysis, we choose four different arbitrary models of strange stars with compactness $u(=\frac{M}{R})$ 0.25, 0.30, 0.35 and 0.40. We observed that all the necessary physical conditions are satisfied and the presented model is quite reasonable to study the strange stars.

In this paper, we consider static spherical structure to develop some anisotropic solutions by employing the extended gravitational decoupling scheme in the background of $f({ℛ},{𝒯},{{ℛ}}_{\gamma \chi }{{𝒯}}^{\gamma \chi })$ gravity, where ${ℛ}$ and ${𝒯}$ indicate the Ricci scalar and trace of the energy–momentum tensor, respectively. We transform both radial as well as temporal metric functions and apply them on the field equations that produce two different sets corresponding to the decoupling parameter $\xi$. The first set is associated with isotropic distribution, i.e. modified Krori–Barua solution. The second set is influenced from anisotropic factor and contains unknowns which are determined by taking some constraints. The impact of decoupling parameter is then analyzed on the obtained physical variables and anisotropy. We also investigate energy conditions and some other parameters such as mass, compactness and redshift graphically. It is found that our solution corresponding to pressure-like constraint shows stable behavior throughout in this gravity for the considered range of $\xi$.

According to standard cosmology, the universe is homogeneous and isotropic at large scales. However, some anisotropies can be observed at the local scale in the universe through various ways. Here, we have studied the Bianchi Type I model by customizing the scale factors to understand the anisotropic nature of the universe. We have considered two cases with slight modifications of scale factors in different directions in the generalized Bianchi Type I metric equation, and compared the results with the $\mathrm{\Lambda }$CDM model and also with available cosmological observational data. Through this study, we also want to predict the possible degree of anisotropy present in the early universe and its evolution to current time by calculating the value of density parameter for anisotropy $({\mathrm{\Omega }}_{\sigma })$ for both low and high redshift $(z)$ along with the possible relative anisotropy that exist among different directions. It is found that there was a relatively higher amount of anisotropy in the early universe and the anisotropic nature of the universe vanishes at the near past and the present epochs. Thus, at near past and present stages of the universe there is no effective distinction between this anisotropic model and the standard $\mathrm{\Lambda }$CDM model.

In this paper, we explore decoupled anisotropic interior solutions for static sphere using extended gravitational decoupling technique in $f({𝒢})$ gravity. We choose Tolman-IV solution as the isotropic interior source describing compact spherical geometry and extend its domains to determine two anisotropic models using some physical constraints. We test physical acceptability of both models for the compact star PSRJ1416-2230 through physical parameters, energy bounds and causality condition. It is observed that both models are physically viable as well as stable. It is also found that the first star model becomes more dense at its core as compared to the second for a small increase in the coupling constant $\xi$.

The major goal of this study is to examine the viability and stability of anisotropic compact stellar objects using the Karmarkar condition in $f({𝒬})$ gravity, where ${𝒬}$ is a scalar of nonmetricity that explains gravitational effects. We consider a static spherical metric in inner and Schwarzschild spacetime in outer regions of the star to analyze the physical attribute of Vela $\mathrm{\text{X}}-1$, SAX J 1808.4−3658, 4U 1608−52, PSR J0348+0432 and 4U 1820−30 compact stars. The unknown parameters are determined through observational values of the radius and mass of the considered compact stars. We take a specific model of this theory to evaluate the energy density, pressure elements, anisotropy, equation of state parameters and energy bounds in inner region of suggested stellar objects. The equilibrium position of these stars is examined through Tolman–Oppenheimer–Volkoff equation and their stability checked by Herrera cracking method and adiabatic index. We find more viable as well as stable compact stars in this modified theory.

This paper is devoted to formulating exact solutions of axially symmetric spacetime through gravitational decoupling technique. For this purpose, we first evaluate an exact solution in the framework of cosmic strings by assuming some additional constraints on the metric coefficients and extend it to obtain two concrete anisotropic cosmological models. We investigate energy conditions as well as the speed of sound constraint to ensure the physical viability of the developed solutions. It is concluded that both anisotropic models meet all the energy bounds as well as stability criterion. The expanding behavior of the universe is also confirmed through different cosmological parameters.

In this paper, we explore a family of exact solutions to the Einstein field equations (EFEs) describing a spherically symmetric, static distribution of fluid spheres with pressure anisotropy in the setting of embedding class one spacetime continuum. A detailed theoretical analysis of this class of solutions for compact stars PSR J16142230, Her X-1, LMC X-4 and 4U 1538-52 is carried out. The solutions are verified by examining various physical aspects, viz., anisotropy, gravitational redshift, causality condition, equilibrium (TOV-equation), stable static criterion and energy conditions, in connection to their cogency. Due to the well-behaved nature of the solutions for a large range of positive real $n$ values, we develop models of above stellar objects and discuss their behavior with graphical representations of the class of solutions of the first two objects extensively. The solutions studied by Fuloria [Astrophys. Space Sci.362, 217 (2017)] for $n=4$ and Tamta and Fuloria [Mod. Phys. Lett. A34, 2050001 (2019), https://doi.org/10.1142/S0217732320500017] for $n=8,12$ are particular cases of our generalized solution.

The main purpose of this paper is to obtain physically stable stellar models coupled with anisotropic matter distribution in the context of $f({ℛ},{\mathrm{\text{T}}}^2)$ theory. For this, we consider a static spherical geometry and formulate modified field equations containing various unknowns such as matter determinants and metric potentials. We then obtain a unique solution to these equations by employing Durgapal–Fuloria ansatz possessing a constant doublet. We also use matching criteria to calculate the values of these constants by considering the Schwarzschild exterior spacetime. Two different viable models of this modified theory are adopted to analyze the behavior of effective matter variables, anisotropy, energy conditions, compactness and redshift in the interiors of Her X-1, PSR J0348-0432, LMC X-4, SMC X-1, Cen X-3, and SAX J 1808.4-3658 star candidates. We also check the stability of these models by using three different physical tests. It is concluded that our considered stars satisfy all the physical requirements and are stable in this modified gravity for the considered parametric values.

This paper deals with the dynamics of cylindrical collapse with anisotropic fluid distribution in the framework of $f({ℛ},{{𝒯}}_{\mu \nu }{{𝒯}}^{\mu \nu })$ gravity. For this purpose, we consider non-static and static cylindrical spacetimes in the inner and outer regions of a star, respectively. To match both geometries at the hypersurface, we consider the Darmois junction conditions. We use the Misner–Sharp technique to examine the impacts of correction terms and effective fluid parameters on the dynamics of a cylindrical star. A correlation between the Weyl tensor and physical quantities is also developed. The conformally flat condition is not obtained due to the influence of anisotropic pressure and higher-order nonlinear terms. Further, we assume isotropic fluid and specific model of this theory which yields the conformally flat spacetime and inhomogeneous energy density. We conclude that the collapse rate reduces as compared to general relativity due to the inclusion of effective pressure and additional terms of this theory.

This paper explores a new embedding anisotropic charged version of a solution to Einstein–Maxwell field equations in four-dimensional spacetime through the Karmarkar conditions and the gravitational decoupling via minimal geometric decoupling (MGD) technique by choosing Pant’s interior solution [Astrophys. Space Sci. 331, 633 (2011)] as a seed solution to coupled system. Later, we integrate the coupled system within the MGD and explore a family of solutions to represent the realistic structure of nonrotating compact objects. Through the matching of the interior solutions so obtained to the exterior Reissner–Nordström metric, we tune the arbitrary constants for feasible models. After that, we subject our model to a rigorous test for a chosen parameter space to verify the physical viability of the solution for the neutron stars in EXO 1785-248 for a range of values of the decoupling constant $\sigma$. Further, we prove that the constant $\sigma$ is inherently connected to critical physical properties such as the gravitational and surface redshifts, compactification factor, mass/radius relation, etc., of the same compact star candidate EXO 1785-248. The solutions thus obtained exhibit physically viable features which are thoroughly demonstrated through graphical plots.

In this paper, we have developed a static charged anisotropic stellar model for a spherically symmetric spacetime geometry. For this, we have considered charged Durgapal V perfect fluid sphere and constructed its anisotropic counterpart by using gravitational decoupling through the minimal geometric deformation (MGD) approach. We have presented physical analysis of the constructed model in details by taking observational data of two different compact stars, namely, SMC X-4 and Vela X-1, into account. All the physical properties such as density, pressure, sound speeds, energy conditions, stability conditions, Tolman–Oppenheimer–Volkoff (TOV) equation, compactness factor, and redshift are found to meet the general criteria required to ensure a well-behaved stellar system.

The effect of model size on fluid flow through fractal rough fractures under shearing is investigated using a numerical simulation method. The shear behavior of rough fractures with self-affine properties was described using the analytical model, and the aperture fields with sizes varying from 25 to 200mm were extracted under shear displacements up to 20mm. Fluid flow through fractures in the directions both parallel and perpendicular to the shear directions was simulated by solving the Reynolds equation using a finite element code. The results show that fluid flow tends to converge into a few main flow channels as shear displacement increases, while the shapes of flow channels change significantly as the fracture size increases. As the model size increases, the permeability in the directions both parallel and perpendicular to the shear direction changes significantly first and then tends to move to a stable state. The size effects on the permeability in the direction parallel to the shear direction are more obvious than that in the direction perpendicular to the shear direction, due to the formation of contact ridges and connected channels perpendicular to the shear direction. The variances of the ratio between permeability in both directions become smaller as the model size increases and then this ratio tends to maintain constant after a certain size, with the value mainly ranging from 1.0 to 3.0.

The aim of this work is to discuss the evolution of compact stars from the view point of a string fluid in Rastall theory using Krori–Barua (KB) metric as interior geometry. The exterior spacetime is considered as Schwarzschild metric while matching of interior and exterior spacetimes lead to coefficients of KB ansatz. The field equations and dynamical variables of the string fluid are explored. We found the values of Rastall parameter $\eta$ for which the dynamical variables satisfy the energy conditions which shows the existence of physical matter. The model is applied to specific physical features including energy conditions, anisotropy, stability, Tolman–Oppenheimer–Volkoff equation, mass function, compactness and redshift of compact stars, in particular, SAX J1808.4-3658, Vela X-12 and Hercules X-1. It is found that the presented model fulfills all the physical requirements and thus, is realistic. We conclude that the string fluid is responsible for the evolution of compact stars in the cosmos.

We investigate the role of bulk and shear viscosity in the spatially homogeneous anisotropic spacetime, in particular, the Kantowski–Sachs (KS) spacetime. General conditions for the bouncing evolution of universe in anisotropic background have been obtained by using the derived propagation equations of expansion scalar, shear scalar and spatial 3-curvature. We show that the presence of shear viscosity in the model prohibits the energy density to attain its extremum in the bouncing model. We explore the qualitative behavior of KS cosmologies by formulating the Einstein’s field equations into a plane-autonomous system of equations by taking dimensionless equation of state. The stability of the system has been investigated by evaluating and analyzing the eigenvalues at the critical points. The stable solutions exist for the system composed of bulk and shear viscosity. The present analysis through dynamical system method illustrates that the universe does not exhibit synchronous bounce with perfect fluid and/or viscous fluids in the KS spacetime.

Hydraulic tortuosity is one of the key parameters for evaluating effective transport properties of natural and artificial porous media. A pore-scale model is developed for fluid flow through porous media based on fractal geometry, and a novel analytical tortuosity–porosity correlation is presented. Numerical simulations are also performed on two-dimensional Sierpinski carpet model. The proposed fractal model is validated by comparison with numerical results and available experimental data. Results show that hydraulic tortuosity depends on both statistical and morphological characteristics of porous media. The exponents for the scaling law between tortuosity and porosity depend on pore size distribution and tortuous fractal dimension. It has been found that hydraulic tortuosity indicates evident anisotropy for asymmetrical particle arrangements under the same statistical characteristics of porous media. The present work may be helpful to understand the transport mechanisms of porous materials and provide guidelines for the development of oil and gas reservoir, water resource and chemical engineering, etc.

This paper investigates the energy bounds in modified Gauss–Bonnet gravity with anisotropic background. Locally rotationally symmetric Bianchi type $I$ cosmological model in $f(R,G)$ gravity is considered to meet this aim. Primarily, a general $f(R,G)$ model is used to develop the field equations. In this aspect, we investigate the viability of modified gravitational theory by studying the energy conditions. We take in account four $f(R,G)$ gravity models commonly discussed in the literature. We formulate the inequalities obtained by energy conditions and investigate the viability of the above-mentioned models using the Hubble, deceleration, jerk and snap parameters. Graphical analysis shows that for first two $f(R,G)$ gravity models, null energy condition (NEC), weak energy condition (WEC) and strong energy condition (SEC) are satisfied under suitable values of anisotropy and model parameters involved. Moreover, SEC is violated for the third and fourth models which predicts the cosmic expansion.