Anisotropic relativistic stellar models

We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the anisotropy factor. The energy density and both radial and tangential pressures are finite and positive inside the anisotropic star. Numerical results show that the basic physical parameters (mass and radius) of the model can describe realistic astrophysical objects like neutron stars.     

Chapman-Enskog-maximum entropy method on time-dependent neutron transport equation

The time-dependent neutron transport equation in semi and infinite medium with linear anisotropic and Rayleigh scattering is proposed. The problem is solved by means of the flux-limited, Chapman-Enskog-maximum entropy for obtaining the solution of the time-dependent neutron transport. The solution gives the neutron distribution density function which is used to compute numerically the radiant energy density E(x,t), net flux F(x,t) and reflectivity R_f. The behaviour of the approximate flux-limited maximum entropy neutron density function are compared with those found by other theories. Numerical calculations for the radiant energy, net flux and reflectivity of the proposed medium are calculated at different time and space.     

Bianchi Type I Viscous Universe with Variable G and Λ

Exact solutions for an anisotropic Bianchi type I model with bulk viscosity and variable G and are obtained. We have found some solutions that correspond to our earlier work for the isotropic one. Unlike Kalligas et al., an inflationary solution with a variable energy density has been found where the anisotropy energy decreases exponentially with time. There is a period of hyper-inflation during which the energy density remains constant.     

Stellar modeling with the Einstein-Maxwell field equations via gravitational decoupling

The aim of the present paper is to find an exact anisotropic and charged version of the well-known Heintzmann interior solution [Z. Phys. 228 (1969) 489] in a space-time via the minimal geometric deformation approach to gravitational decoupling (MGD-decoupling). Further, we discuss the physical cogency of the solution for the coupled system by performing several physical tests. The obtained model represents the neutron star 4U1608-52 and fulfills all the requirements in order to be a well behaved physical solution to Einstein-Maxwell’s field equations.     

Effects of charge on gravitational decoupled anisotropic solutions in f(R) gravity

This paper is devoted to studying charged anisotropic static spherically symmetric solutions through gravitationally decoupled minimal geometric deformation technique in f(R) gravity. For this purpose, we first consider the known isotropic Krori–Barua solution for f(R) Starobinsky model in the interior of a charged stellar system and then include the effects of two types of anisotropic solutions. The corresponding field equations are constructed and the unknown constants are obtained from junction conditions. We analyze the physical viability and stability of the resulting solutions through effective energy density, effective radial/tangential pressure, energy conditions, and causality condition. It is found that both solutions satisfy the stability range as well as other physical conditions for specific values of charge as well as model parameter and anisotropic constant. We conclude that the modified theory under the influence of charge yields more stable behavior of the self-gravitating system.     

Anisotropic static solutions in modelling highly compact bodies

Einstein field equations for static anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities. Two classes of solutions are possible. The first class contains the limiting caseμ,∝ r^-2 for the energy density which arises in many astrophysical applications. In the second class the singularity at the centre of the star is not present in the energy density.     

Binding energy for inhomogeneous nuclear matter

For a spatial finite nuclear density distribution a binding energy formula is developed. A modified Thomas-Fermi method which deduces the mixed density by taking into account an anisotropic local momentum space occupation is used. This method presents the binding energy as a functional of the proton and neutron density distributions. It was possible within this framework to derive in a consistent way the energy correction terms due to density inhomogeneities. The structure of these energy correction terms is shown and an estimate is given for the adjustable parameters of this model to fit the experimental nuclear masses.     

Cosmological constant in the Bianchi type-I-modified Brans-Dicke cosmology

In 1961, Brans and Dicke [1] provided an interesting alternative to general relativity based on Mach’s principle. To understand the reasons leading to their field equations, we first consider homogeneous and isotropic cosmological models in the Brans-Dicke theory. Accordingly we start with the Robertson-Walker line element and the energy tensor of a perfect fluid. The scalar field φ is now a function of the cosmic time only. Then we consider spatially homogeneous and anisotropic Bianchi type-I-cosmological solutions of modified Brans-Dicke theory containing barotropic fluid. These have been obtained by imposing a condition on the cosmological parameter Λ(φ). Again we try to focus the meaning of this cosmological term and to relate it to the time coordinate which gives us a collapse singularity or the initial singularity. On the other hand, our solution is a generalization of the solution found by Singh and Singh [2]. As far as we are aware, such solution has not been given earlier.     

Static anisotropic fluid spheres in general relativity with nonuniform density

An Ansatz developed by Maharaj and Maartens is used to obtain solutions of Einstein's field equations for static anisotropic fluid spheres with nonuniform density. These solutions are matched with the Schwarzschild exterior solution.     

Equation of state for anisotropic spheres

We present a new class of exact interior solutions for anisotropic spheres to the Einstein field equations with a prescribed energy density. This category of solutions has similar energy density profiles to the models of Chaisi and Maharaj (Gen. Rel. Grav. 37, 1177–1189, 2005) whose approach we follow in the integration process. A distinguishing feature of the solutions presented is that they satisfy a barotropic equation of state linearly relating the radial pressure to the energy density.     

Decoupled anisotropic spheres in self-interacting Brans-Dicke gravity

The focus of this paper is to obtain anisotropic spherically symmetric solutions by means of gravitational decoupling in the background of self-interacting Brans-Dicke theory. We introduce minimal geometric deformation in the radial metric component to decouple the field equations into two arrays. The first set, governed by the seed source, is determined through metric functions of isotropic solution (Heintzmann/Tolman VII spacetimes) while the second set is solved by imposing two constraints on the anisotropic source. The unknown constants are evaluated via matching conditions at the stellar boundary. We investigate the effects of massive scalar field as well as decoupling parameter on the physical structure of anisotropic models and check them for viability through energy conditions. It is concluded that the anisotropic solutions obtained through constraint I are well-behaved for selected values of the decoupling parameter. For the second constraint, the extended Heintzmann solution is viable but anisotropic Tolman solution does not comply with dominant energy condition for higher values of the decoupling parameter.     

General relativistic electromagnetic mass models of neutral spherically symmetric systems

The recent work of Grøn [1] concerning charged analogues of Florides' class of solutions is discussed and generalized. The properties of this kind of model are investigated. In particular it is shown that the ratiom/r as well as the acceleration of gravity are maximum inside the body rather than at the boundary. Some exact solutions of the Einstein-Maxwell equations illustrating these properties are presented. The solutions are matched continuously to the exterior Schwarzschild solution and they represent electromagnetic mass models of neutral systems. All physical quantities are finite inside the distributions. The energy density is positive and decreases monotonically from its maximum value at the center to zero at the boundary.     

托卡马克中逃逸电子分布函数和波能密度计算

本文用非等距有限差分法,求解了准线性微分方程组,获得了在电子平行速度区间,逃逸电子分布函数和波能密度的二维演化图象。这一结果比文[1]和[2]在稳态情形下所得到的解析结果以及文[1]在一维情形下演化的解析结果,较完整地反映了逃逸电子分布函数的特征。可供对逃逸电子的进一步研究参考。     

2+1-dimensional gravitational decoupled anisotropic solutions

This paper investigates exact models for spherically symmetric anisotropic matter distribution in 2+1-dimensions via gravitational decoupling approach. For this purpose, we choose known spherical solutions with perfect fluid in the absence as well as the presence of cosmological constant and extend them to anisotropic models by imposing a constraint on matter components. The physical viability and stability of our developed solutions are investigated through graphical analysis of density, radial/tangential pressure, energy conditions, and causality criterion. It is found that both solutions are stable and satisfy all the physical requirements for the feasible choice of the model parameters.     

Gravitational decoupled charged anisotropic solutions in modified Gauss-Bonnet gravity

This paper is devoted to the study of charged anisotropic exact solutions for spherical geometry in the context of modified Gauss-Bonnet gravity using the gravitational decoupling technique. We take Krori-Barua solution in the presence of charge for a spherically symmetric self-gravitating system and extend it to obtain two anisotropic solutions through some constraints. We study the stability as well as the physical viability criterion of the resulting solutions using anisotropy, squared speed of sound parameter and energy bounds. Both models turn out to be physically viable and stable as they fulfill the required energy conditions and stability criterion. We conclude that the stability of both anisotropic solutions increases with a decrease in charge.     

Exact inhomogeneous Einstein-Liouville solutions in Robertson-Walker space-times

We give the general solution of Liouville's equation in Robertson-Walker space-times, and use this to find exact inhomogeneous Einstein-Liouville solutions, using the covariant harmonic method of Ellis, Matravers and Treciokas [1]. The average four-velocity of the gas is tilted, and the gas has nonzero acceleration, shear, energy flux, and anisotropic stress.     

A phase field model of deformation twinning: Nonlinear theory and numerical simulations

A continuum phase field theory and corresponding numerical solution methods are developed to describe deformation twinning in crystalline solids. An order parameter is associated with the magnitude of twinning shear, i.e., the lattice transformation associated with twinning. The general theory addresses the following physics: large deformations, nonlinear anisotropic elastic behavior, and anisotropic phase boundary energy. The theory is applied towards prediction of equilibrium phenomena in the athermal and non-dissipative limit, whereby equilibrium configurations of an externally stressed crystal are obtained via incremental minimization of a free energy functional. Outcomes of such calculations are elastic fields (e.g., displacement, strain, stress, and strain energy density) and the order parameter field that describes the size and shape of energetically stable twin(s). Numerical simulations of homogeneous twin nucleation in magnesium single crystals demonstrate fair agreement between phase field solutions and available analytical elasticity solutions. Results suggest that critical far-field displacement gradients associated with nucleation of a twin embryo of minimum realistic size are 4.5%–5.0%, with particular values of applied shear strain and equilibrium shapes of the twin somewhat sensitive to far-field boundary conditions and anisotropy of twin boundary surface energy.     

The behaviour of vortex lines near the surfaces of a uniaxial anisotropic superconducting quarter space

The behaviour of the distorted vortex lattice near the surfaces of a uniaxial anisotropic superconducting quarter-space is studied. The analytical solution of the distributions of the fields inside and outside the sample as well as the current density are calculated in an integral form. Using these solutions, the forces on the vortex segments are completely determined. The Gibbs free energy of the system is investigated in a simple form. Agreement with previous results is found in the isotropic limiting case. Moreover, in some limiting cases, good agreement with the results obtained for a high temperature superconducting semi-infinite space is achieved.     

The discrete ordinates method for anisotropic scattering in the neutron transport theory: The critical sphere problem

The spherical harmonics method for anisotropic scattering in the neutron transport theory related to the critical sphere problem was investigated by Yildiz [The spherical harmonics method for anisotropic scattering in neutron transport theory: the critical sphere problem. JQSRT 2001;71:25-37]. Some numerical results and figures that they provided are incorrect. The correct numerical results for the critical radius are obtained and tabulated for different scattering parameters by using the discrete ordinates method.