Narrow Results

This paper explores a comprehensive approach to modeling compact stars that incorporates both normal matter and dark energy. We employ the Durgapal–Fuloria ansatz within the context of Rastall gravity to derive a relativistic analytical solution. The model is thoroughly analyzed both analytically and graphically, to assess its physical properties and facilitates a comparison with the results of classical general relativity. Our findings demonstrate that the model we have put forward is in substantial agreement with observational data for three different compact star representatives like Her X-1, PSR J0348+0432, and RX J1856.3-37.2. We evaluate the model’s viability by examining its energy conditions, stability, and adherence to the Buchdahl limit, all of which are found to be satisfactory. The analysis confirms the stable solution for Rastall parameter spanning −0.005 to 0.11, and it converges to standard general relativity when the coupling parameter approaches to zero.

This paper describes a new computational method of fully automated anisotropic triangulation of a trimmed parametric surface. Given as input: (1) a domain geometry and (2) a 3×3 tensor field that specifies a desired anisotropic node-spacing, this new approach first packs ellipsoids closely in the domain by defining proximity-based interacting forces among the ellipsoids and finding a force-balancing configuration using dynamic simulation. The centers of the ellipsoids are then connected by anisotropic Delaunay triangulation for a complete mesh topology. Since a specified tensor field controls the directions and the lengths of the ellipsoids' principal axes, the method generates a graded anisotropic mesh whose elements conform precisely to the given tensor field.

Waves propagating through heterogeneous media experience scattering that can convert a coherent pulse into small incoherent fluctuations. This may appear as attenuation for the transmitted front pulse. The classic O’Doherty–Anstey theory describes such a transformation for scalar waves in finely layered media. Recent observations for seismic waves in the earth suggest that this theory can explain a significant component of seismic attenuation. An important question to answer is then how the O’Doherty–Anstey theory generalizes to seismic waves when several wave modes, possibly with the same velocity, interact. An important aspect of the O’Doherty–Anstey theory is the statistical stability property, which means that the transmitted front pulse is actually deterministic and depends only on the statistics of the medium but not on the particular medium realization when the medium is modeled as a random process. It is shown in this paper that this property generalizes in the case of elastic waves in a nontrivial way: the energy of the transmitted front pulse, but not the pulse shape itself, is statistically stable. This result is based on a separation of scales technique and a diffusion-approximation theorem that characterize the transmitted front pulse as the solution of a stochastic partial differential equation driven by two Brownian motions.

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.

We present perfect fluid Bianchi type-I cosmological models with time-dependent cosmological term $\mathrm{\Lambda }$. Exact solutions of the Einstein’s field equations are presented via a suitable functional form for Hubble parameter $H$, which yields a model of the universe that represents initially decelerating and late-time accelerating expansion. We discuss, in the context of some vacuum decay laws, cosmological implications of the corresponding solutions. The physical and geometrical features of the models are also discussed.

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.

This paper is devoted to exploring exact charged solutions in a cloud of strings through minimal geometric deformation technique in three-dimensional gravity. For this purpose, we first evaluate the exact charged isotropic solution for static circular symmetry using Takabayashi equation of state and extend it to obtain three concrete anisotropic charged models. We investigate energy conditions as well as speed of sound constraint to check the viability of the respective solutions. It is concluded that the second model is a realistic one as it fulfills all the physical characteristics as well as stability criterion while the rest of two solutions do not satisfy the physical constraints.

In this paper, a well-behaved new model of anisotropic compact star in (3+1)-dimensional spacetime has been investigated in the background of Einstein’s general theory of relativity. The model has been developed by choosing $g_{rr}$ component as Krori–Barua (KB) ansatz [Krori and Barua in J. Phys. A, Math. Gen. 8 (1975) 508]. The field equations have been solved by a proper choice of the anisotropy factor which is physically reasonable and well behaved inside the stellar interior. Interior spacetime has been matched smoothly to the exterior Schwarzschild vacuum solution and it has also been depicted graphically. Model is free from all types of singularities and is in static equilibrium under different forces acting on the system. The stability of the model has been tested with the help of various conditions available in literature. The solution is compatible with observed masses and radii of a few compact stars like Vela X-1, 4U $1608-52$, PSR J$1614-2230$, LMC X$-4$, EXO $1785-248$.

This paper investigates the new interior solution of stellar compact spheres in the framework of metric $f(R)$ gravity. In this connection, we derived the Einstein field equations for static anisotropic spherically symmetric spacetime in the mechanism of Karmakar condition. The obtained results of the field equations have been studied with well-known Starobinskian model $f(R)=R+\zeta R^2$ by using three different compact stars like RXJ1856-37, $\mathrm{\text{Her}}X$-$1$, $\mathrm{\text{Vela}}X$-$12$. Moreover, the constants involved in the solution of metric potentials have been determined through smooth matching conditions between the interior geometry and exterior spacetime. Thereafter, the physical significance of the obtained results is examined in the form of fluid variables, equation of state (EoS) parameters, energy conditions, anisotropic stress and stability analysis by using the graphical plot. The approximated values of the constants and the mass-radius relation have been calculated through different stellar star objects ($\mathrm{\text{RXJ}}1856$-$37$ ($r_b=6\mathrm{\text{Km}}$), $\mathrm{\text{Her}}X$-$1$ ($r_b=6.7\mathrm{\text{Km}}$) and $\mathrm{\text{Vela}}X$-$12$ ($r_b=9.99\mathrm{\text{Km}}$)) shown in Table 1. Finally, we have concluded that our considered compact stellar objects with particular choice of $f(R)$ model in the mechanism of Karmakar condition satisfies all the necessary bounds for potentially stable formation of the stars.

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.

In this paper, we derive the exact solution of traversable wormholes illustrating spherically symmetric geometry with anisotropic matter distribution entering the throat in the formalism of $f({ℛ},{𝒯})$ gravity, where ${ℛ}$ is Ricci scalar and ${𝒯}$ is trace of energy–momentum tensor. For this purpose, we assume a power law-type generic function $f({ℛ},{𝒯})={ℛ}+\gamma {{ℛ}}^2+\alpha {𝒯}$, where $\gamma$ and $\alpha$ are being constants, with two different choices of shape functions $a(r)=r_0(\frac{b^r}{b^{r_0}}),0<a(r)<1$ and $a(r)=r_0{(\frac{cosh(r_0)}{cosh(r)})}^{\mu },0<\mu <1$. For each approach, we find the exact solution and studied the existence of wormhole solutions in the presence of exotic and non-exotic matter. The graphical behavior of equation of state (EoS) parameter and energy condition bounds is also investigated for each shape function. The realistic wormhole solutions are obtained for the shape functions which satisfy necessary conditions at the throat radius $r=r_0=1$. Finally, we observe that there is small deviation in the results obtained by General Relativity and $f({{ℛ}}^2,{𝒯})$ gravity.

In this paper, we aim to formulate anisotropic solutions that represent charged self-gravitating static spheres in $f(R)$ gravity. We introduce the effects of anisotropy in the domain of an isotropic solution by including an extra matter source. The spherical configuration is deformed by transforming radial as well as temporal metric functions. As a result of these transformations, the isotropic and anisotropic matter sources can be decoupled from each other. The system of field equations is disintegrated into two arrays such that the first set corresponds to the isotropic source while the second comprises the new gravitational source. The charged Krori–Barua spacetime is employed to specify the first set in the background of $f(R)$ Starobinsky model. Two solutions of the other system are determined by incorporating a barotropic equation of state along with additional constraints on the anisotropic source. The matching conditions are imposed at the hypersurface to determine the values of unknown constants. Different features of the constructed models are inspected by using the mass and radius of Her X-I. One of the constructed solutions agrees with the viability and stability conditions for specific values of charge and the decoupling parameter.

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.

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.

In this paper, a class of anisotropic compact stars is analyzed in Heintzmann geometry. The Einstein field equations (EFEs) have been solved to obtain the stellar model in presence of pressure anisotropy. We have considered the $g_{tt}$ metric component as proposed by Heintzmann, and by solving the EFEs, the $g_{rr}$ metric component is evaluated in the presence of pressure anisotropy. It is noted that for an isotropic star ($\alpha =0$), the maximum mass lies within the range 1.87–3.04$M_{\odot }$ for radii ranging between 8–13 km. For anisotropic compact stars, the maximum mass increases with $\alpha$ and lies within the range 1.99–3.23 $M_{\odot }$ for anisotropy parameter $\alpha =0.5$. The physical viability of the model is examined by applying our model to study the properties of a few known compact objects. All the stability conditions are fulfilled in the proposed model. It is also interesting to note that the maximum mass calculated from our model from geometrical consideration and solving the TOV equation is approximately equal, and the radii predicted from the present model comply with the estimated radius from observations of recently observed pulsars and lighter compact objects of GW events such as GW 190814 and GW 170817.

Anisotropy of a Gaussian field with stationary increments is related with the anisotropy of its spectral density. Such Gaussian fields can be used for modelling anisotropic homogeneous media, which leads to try to simulate these ones and identify parameters. This paper is a first attempt in these two directions. We first show how such Gaussian fields can be written as a random series, which is a first step for simulation purposes. There is anisotropy of the Gaussian field when its spectral density has a different power law in each direction. The exponent in a given direction can be obtained from an integration of the field on the orthogonal hyperplanes, as proved by the two last authors in ⁴. We then show how this property can be used to propose an estimator of this exponent.