Anisotropic Solutions Research Articles

Effects of non-minimal matter-geometry coupling on embedding class-one anisotropic solutions

This paper investigates some particular anisotropic star models in gravity, where . We adopt a standard model , where ϖ indicates a coupling constant. We take spherically symmetric spacetime and develop solutions to the modified field equations corresponding to different choices of the matter Lagrangian by applying ‘embedding class-one’ scheme. For this purpose, we utilize bag model equation of state and investigate some physical aspects of compact models such as RXJ 1856-37, 4U 1820-30, Cen X-3, SAX J 1808.4-3658 and Her X-I. We use masses and radii of these stars and employ the vanishing radial pressure condition at the boundary to calculate the value of their respective bag constant . Further, we fix ϖ = ± 4 to analyze the behavior of resulting state variables, anisotropy, mass, compactness, surface redshift as well as energy bounds through graphical interpretation for each star model. Two different physical tests are performed to check the stability of the developed solutions. We conclude that ϖ = −4 is more suitable choice for the considered modified model to obtain stable structures of the compact bodies.

Physical viability of anisotropic compact stars solutions under Karmarkar condition in f(ℛ,𝒯) theory of gravity

In this paper, we investigate the generalized symmetric, static compact objects under anisotropic fluid in the background of Karmarkar embedding class-1 condition. To find the exact solutions of the modified field equations, we consider the gravitational Lagrangian as a linear function of the Ricci scalar and the trace of the stress–energy tensor, i.e. [Formula: see text], where [Formula: see text] is a constant. By employing the concept of Karmarkar condition, we calculate a [Formula: see text] metric component, while for a specific form of [Formula: see text], the gravitational potential is chosen. To attain the closed-form solutions of the modified field equations, we match the interior spacetime metric with the exterior Schwarzschild metric at the boundary and using the numerical values of mass and radius of the compact stars like PSR J1903+327, 4U 1820-30, LMC X-4, and EXO 1785-248, we constraint some unknown parameters. We have discussed physical stability of the stellar configuration by adopting the energy bounds, Tolman–Oppenheimer–Volkov (TOV) equation, adiabatic index, central density and pressure as well. It is concluded that our resulting anisotropic solutions did well behave and a reasonable degree of precision with recent observations.

Isotropic and complexity-free deformed solutions in self-interacting Brans–Dicke gravity

In this work, we focus on constructing two analogs of an anisotropic seed solution via the decoupling technique. For this purpose, we add a new matter source alongside the anisotropic fluid in a static sphere. A transformation in the radial metric component is applied to split the field equations into two sets such that the influence of each source is limited to one array. The anisotropic solution constructed by employing the embedding class-one condition is used to specify the set corresponding to the seed source. We obtain two solutions of the second set (related to the additional source) by applying constraints on the anisotropy and complexity of the self-gravitating system. A smooth junction between the interior and exterior spacetimes determines the unknown constants. Various physical characteristics, such as viability and stability, are graphically analyzed by utilizing the radius and mass of the star PSR J1614-2230. It is found that the extended solutions agree with the energy conditions as well as stability criteria for selected values of the parameters.

Laplace domain BEM for anisotropic transient elastodynamics

In this paper, we describe Laplace domain boundary element method (BEM) for transient dynamic problems of three-dimensional finite homogeneous anisotropic linearly elastic solids. The employed boundary integral equations for displacements are regularized using the static traction fundamental solution. Modified integral expressions for the dynamic parts of anisotropic fundamental solutions and their first derivatives are obtained. Boundary elements with mixed approximation of geometry and field variables with the standard nodal collocation procedure are used for spatial discretization. In order to obtain time-domain solutions, the classic Durbin’s method is applied for numerical inversion of Laplace transform. Problem of alleviating Gibbs oscillations is addressed. Dynamic boundary element analysis of the model problem involving trigonal material is performed to test presented formulation. Obtained results are compared with finite element solutions.

Anisotropic solution of the holographic model of light quarks with an external magnetic field

Anisotropic solution of the holographic model of light quarks with an external magnetic field

Wormholes in a viscous universe

We study the static and spherically symmetric wormhole spacetime configurations at present time in a viscous universe. Considering three classes of viscous models, i.e., bulk viscosity as a function of Hubble constant $H_0$, present cosmic temperature $T_0$ and dark energy density $\rho_0$, respectively, we obtain several wormhole solutions. Through the analysis for the anisotropic solutions, we conclude that, to some extent, these three classes of viscous models have very high degeneracy with each other, and deviate slightly from the ideal fluid consequence. Subsequently, without the loss of generality, to investigate the traversabilities, energy conditions and stability for the wormhole solution, we study the wormhole solution of the constant redshift function of the viscous $\omega$CDM model with a constant bulk viscosity coefficient. We obtain the following conclusions: the value of traversal velocity decreases for decreasing bulk viscosity, and the traversal velocity for a traveler depends on not only the wormhole geometry but also the effects of cosmological background evolution; the null energy condition will be violated more clearly when the bulk viscosity or the cosmic expansion velocity decreases; for the case of a positive surface energy density, the range of the junction radius decreases and the values of the parameter $\lambda$ are further restricted when the throat radius of the wormhole $r_0/M$ increases, bulk viscosity coefficient $\zeta_0$ decreases and present-day Hubble parameter $H_0$ decreases, respectively; for the case of a negative surface energy density, by increasing $r_0/M$, decreasing $\zeta_0$ and increasing $H_0$, the values of the parameter $\lambda$ are less restricted, one may conclude that the total stability region increases, and the range of the junction radius increases, increases and decreases, respectively. \end{abstract}

Anisotropic stellar solutions in torsion-trace gravity under Karmarkar condition

In this paper, we formulate exact anisotropic interior solutions of the Einstein field equations preserving spherically symmetric geometry in the context of [Formula: see text] gravity. To make the system close, we consider a linear function in torsion scalar [Formula: see text] and trace of energy–momentum tensor [Formula: see text], and employ the well-known Karmarkar condition with metric potential of the form [Formula: see text]. We consider standard data of some well-known compact star models (Vela X-1, PSR J1614-2230, Cen X-3 and EXO 1785-248) to estimate the unknown model parameters. We perform physical analysis of the developed model in detail, which includes density profile, pressure profile, anisotropy factor, mass function, gravitational/surface redshift, compactness factor, energy bounds, stability criteria, and the equilibrium condition. The analysis leads us to conclude that solutions are well-behaved and physically viable.

Calculating the isotropic and anisotropic roughness by using MW model: A variable thermal conductivity study

In this paper, we analyze the mathematical and theoretical studies of flow over a heated rough rotating disk. By using the Carreau fluid model we examine the dilatant and pesudoplastic behavior along with mean flow under the partial slip conditions. The variable fluid property is considered for heat phenomena. This study has stimulated a great deal of interest in applied engineering due to its enhanced theoretical and mathematical advantages. We analyzed the isotropic and anisotropic solutions for Carreau fluid model with variable fluid property. The similarity transformations used here for the Carreau fluid was initially presented by von Kàrmàn, it reduces the boundary layer equations into ordinary differential equations. Shooting method is used to solve the dimensionless ordinary differential equations. All of the obtained outcomes are analyzed for the mean flow velocity and temperature profiles and physical characteristics are shown in the form of graphs and table.

Anisotropic hyperbolic inflation for a model of two scalar and two vector fields

In this paper, we extend a recent proposed model of two scalar and two vector fields to a hyperbolic inflation scenario, in which the field space of two scalar fields is a hyperbolic space instead of a flat space. In this model, one of the scalar fields is assumed to be a radial field, while the other is set as an angular field. Furthermore, both scalar fields will be coupled to two different vector fields, respectively. As a result, we are able to obtain a set of exact Bianchi type I solutions to this model. Stability analysis is also performed to show that this set of anisotropic solutions is indeed stable and attractive during the inflationary phase. This result indicates that the cosmic no-hair conjecture is extensively violated in this anisotropic hyperbolic inflation model.

Determining the charge distribution and the direction of bond cleavage with femtosecond anisotropic x-ray liquidography

Energy, structure, and charge are fundamental quantities characterizing a molecule. Whereas the energy flow and structure change in chemical reactions are experimentally characterized, determining the atomic charges of a molecule in solution has been elusive, even for a triatomic molecule such as triiodide ion, I3−. Moreover, it remains to be answered how the charge distribution is coupled to the molecular geometry; which I-I bond, if two I-I bonds are unequal, dissociates depending on the electronic state. Here, femtosecond anisotropic x-ray solution scattering allows us to provide the following answers in addition to the overall rich structural dynamics. The analysis unravels that the negative charge of I3− is highly localized on the terminal iodine atom forming the longer bond with the central iodine atom, and the shorter I-I bond dissociates in the excited state, whereas the longer one in the ground state. We anticipate that this work may open a new avenue for studying the atomic charge distribution of molecules in solution and taking advantage of orientational information in anisotropic scattering data for solution-phase structural dynamics.

Study of Decoupled Anisotropic Solutions in f(R, T, RρηTρη) Theory

In this paper, we consider isotropic solution and extend it to two different exact well-behaved spherical anisotropic solutions through minimal geometric deformation method in f(R,T,RρηTρη) gravity. We only deform the radial metric component that separates the field equations into two sets corresponding to their original sources. The first set corresponds to perfect matter distribution while the other set exhibits the effects of additional source, i.e., anisotropy. The isotropic system is resolved by assuming the metric potentials proposed by Krori-Barua while the second set needs one constraint to be solved. The physical acceptability and consistency of the obtained solutions are analyzed through graphical analysis of effective matter components and energy bounds. We also examine mass, surface redshift and compactness of the resulting solutions. For particular values of the decoupling parameter, our both solutions turn out to be viable and stable. We conclude that this curvature-matter coupling gravity provides more stable solutions corresponding to a self-gravitating geometry.

Regular interior solutions to the solution of Kerr which satisfy the weak and the strong energy conditions

The line element of a class of solutions that match the solution of Kerr on an oblate spheroid if the two functions F(r) and H(r) on which it depends satisfy certain matching conditions is presented. The non-vanishing components of the Ricci tensor Rμν, the Ricci scalar R, the second order curvature invariant K, the eigenvalues of the Ricci tensor, the energy density μ, the tangential pressure P⊥, and the quantity μ + P⊥ are calculated. A function F(r) is given for which R and K and therefore the solutions are regular. The function H(r) should be such that the solution it gives satisfies at least the Weak Energy Conditions (WEC). Several H(r) are given explicitly for which the resulting solutions satisfy the WEC and also the strong energy conditions, and the graphs of their μ, P⊥, and μ + P⊥ for certain values of their parameters are presented. It is shown that all solutions of the class are anisotropic fluid solutions and that there are no perfect fluid solutions in the class.

Role of gravitational decoupling on isotropization and complexity of self-gravitating system under complete geometric deformation approach

In the present paper, we discuss the role of gravitational decoupling to isotropize the anisotropic solution of Einstein’s field equations in the context of the complete geometric deformation (CGD) approach and its influence on the complexity factor introduced by Herrera (Phys Rev D 97:044010, 2018) in the static self-gravitating system. Moreover, we proposed a simple and effective technique as well to generate new solutions for self-gravitating objects via CGD approach by using two systems with the same complexity factor and vanishing complexity factor proposed by Casadio et al. (Eur Phys J C 79:826, 2019). The effect of decoupling constant and the compactness on the complexity factor have also been analyzed for the obtained solutions.

A homogenised model for flow, transport and sorption in a heterogeneous porous medium

A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for this purpose. Here, we consider a two-dimensional microstructure comprising an array of obstacles of smooth but arbitrary shape, the size and spacing of which can vary along the length of the porous medium. We use homogenisation via the method of multiple scales to systematically upscale a novel problem involving cells of varying area to obtain effective continuum equations for macroscale flow and transport. The equations are characterised by the local porosity, a local anisotropic flow permeability, an effective local anisotropic solute diffusivity and an effective local adsorption rate. These macroscale properties depend non-trivially on the two degrees of microstructural geometric freedom in our problem: obstacle size and obstacle spacing. We exploit this dependence to construct and compare scenarios where the same porosity profile results from different combinations of obstacle size and spacing. We focus on a simple example geometry comprising circular obstacles on a rectangular lattice, for which we numerically determine the macroscale permeability and effective diffusivity. We investigate scenarios where the porosity is spatially uniform but the permeability and diffusivity are not. Our results may be useful in the design of filters or for studying the impact of deformation on transport in soft porous media.

Generalized compact star models with conformal symmetry

We generate a new generalized regular charged anisotropic exact model that admits conformal symmetry in static spherically symmetric spacetime. Our model was examined for physical acceptability as realistic stellar models. The regularity is not violated, the energy conditions are satisfied, the physical forces balanced at equilibrium, the stability is satisfied via adiabatic index, and the surface red shift and mass–radius ratio are within the required bounds. Our conformal charged anisotropic exact solution contains models generated by Finch–Skea, Vaidya–Tikekar and Schwarzschild. Also, some recent charged or neutral and anisotropic or isotropic conformally symmetric models are found as special cases of our exact model. Our approach using a conformal symmetry provides a generalized geometric framework for studying compact objects.

Self-gravitating anisotropic star using gravitational decoupling

This paper addresses a new gravitationally decoupled anisotropic solution for the compact star model via the minimal geometric deformation (MGD) approach. We consider a non-singular well-behaved gravitational potential corresponding to the radial component of the seed spacetime and embedding Class I condition that determines the temporal metric function to solve the seed system completely. However, two different well-known mimic approaches such as and have been employed to determine the deformation function which gives the solution of the second system corresponding to the extra source. In order to test the physical viability of the solution, we have checked several conditions such as regularity conditions, energy conditions, causality conditions, hydrostatic equilibrium, etc. Moreover, the stability of the solutions has been also discussed by the adiabatic index and its critical value. We find that the solutions set seems viable as far as observational data are concerned.

Gravitational decoupled anisotropic spherical solutions in f(R, T) gravity by minimal geometric deformation approach

This article deals with the new systematic approach that is gravitational decoupling via minimal geometric deformation (MGD) approach. Here, we present the anisotropic spherical solution in f(R, T) gravity by adopting MGD approach. For this, we consider the Tolman V isotropic solution and extend it to anisotropic domain. For comprehensive results in f(R, T) theory, we assume viable model which is a linear combination of generalized Starobinsky f(R) model (Starobinsky 1980 Phys. Lett. B 91, 99) and λT (where T is the trace of T ij ). We are producing two different versions of anisotropic solution adopting two different mimic constraints. This technique helps us to find the new groups of anisotropic solutions through a single isotropic solution. We analyze the physical behavior of the anisotropic solutions through energy conditions and causality conditions. The graphical representation shows that both solutions satisfy all the energy conditions for different ranges of parameters. We conclude that both obtained models present the realistic behavior satisfying the all physical constraints and stability criterion.

Charged anisotropic compact stellar solutions in torsion-trace gravity via modified chaplygin gas model

Charged anisotropic compact stellar solutions in torsion-trace gravity via modified chaplygin gas model

Anisotropic spacetimes in chiral scalar field cosmology

Study the behaviour and the evolution of the cosmological field equations in an homogeneous and anisotropic spacetime with two scalar fields coupled in the kinetic term. Specifically, the kinetic energy for the scalar field Lagrangian is that of the Chiral model and defines a two-dimensional maximally symmetric space with negative curvature. For the background space we assume the locally rotational spacetime which describes the Bianchi I, the Bianchi III and the Kantowski-Sachs anisotropic spaces. We work on the $H$% -normalization and we investigate the stationary points and their stability. For the exponential potential we find a new exact solution which describes an anisotropic inflationary solution. The anisotropic inflation is always unstable, while future attractors are the scaling inflationary solution or the hyperbolic inflation. For scalar field potential different from the exponential, the de Sitter universe exists.

Anisotropic constant-roll inflation for the Dirac\u2013Born\u2013Infeld model

In this paper, we study a non-canonical extension of a supergravity-motivated model acting as a vivid counterexample to the cosmic no-hair conjecture due to its unusual coupling between scalar and electromagnetic fields. In particular, a canonical scalar field is replaced by the string-inspired Dirac–Born–Infeld one in this extension. As a result, exact anisotropic inflationary solutions for this Dirac–Born–Infeld model are figured out under a constant-roll condition. Furthermore, numerical calculations are performed to verify that these anisotropic constant-roll solutions are indeed attractive during their inflationary phase.