Anisotropic Matter Distribution Research Articles

Anisotropic generalization of Vaidya-Tikekar superdense stars

We study superdense relativistic stars with anisotropic matter distributions with spheroidal spatial hypersurfaces. We propose a methodology to make an anisotropic generalization of the Vaidya-Tikekar superdense star model. The anisotropic Einstein field equations can be solved in terms of hypergeometric functions for our choice of gravitational potential and anisotropy. Particular parameter choices allow us to generate models of anisotropic stars in terms of elementary functions. Also, isotropic stars can be generated in the limit of vanishing anisotropy. In particular, we obtain the well known superdense models of Tikekar which are isotropic and have specific spheroidal geometries. The impact of anisotropy on the gross physical behaviour of a compact star is studied.

Effect of pressure anisotropy on Buchdahl-type relativistic compact stars

We consider exact models for dense relativistic stars with anisotropic pressures and containing Buchdahl-type spacetime geometry. The Buchdahl condition can be transformed to an Euler–Cauchy equation for the gravitational potentials. We solve this condition to find a new exact solution to the Einstein field equations with anisotropic matter distribution. We show that the exact solution produces a realistic model of a compact relativistic star satisfying all physical requirements. The regularity, equilibrium, casuality, stability, energy conditions and compactness limits for a well behaved compact sphere are satisfied.

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.

New classes of generalized anisotropic polytropes pertaining radiation density

In this article, we consider the generalized polytropic equation of state with anisotropic matter distribution in isotropic coordinates. The static spherically symmetric configuration is considered for the development of mathematical models of compact objects incorporating the radiation factor. We have examined 12 different stars with the developed models. Analysis of the models shows that they are well-behaved and physically viable.

Stellar systems and structure scalars

The work is devoted to analyzing the effects of dark source polynomial curvature corrections in the mathematical modeling of radiating stars. In this scenario, we have used a particular f(R, T) model and consider the spherically symmetric geometry of relativistic interior. We assumed that our geometry is coupled with anisotropic shearing matter distribution undergoing radiating epoch with free streaming and diffusion approximation. We have calculated spherically symmetric total matter content with the help of Misner–Sharp formalism. A particular relation among anisotropic pressure, shearing viscosity, radiating parameters, energy density, and tidal forces is obtained. We then expressed this equation with the help of f(R, T) structure scalar, the scalar obtained by orthogonal decomposition of the Riemann tensor. The role of the logarithmic Ricci and trace of stress–energy tensor terms are also observed through Weyl scalar, shear, expansion scalar differential equations.

Relativistic model for anisotropic compact stars using Karmarkar condition

In this work we have obtained some families of relativistic anisotropic compact stars by solving of Einstein’s field equations. The field equations have been solved by suitable particular choice of the metric potential $e^{\lambda }$ and embedding class one condition. The physical analysis of this model indicates that the obtained relativistic stellar structure for anisotropic matter distribution is physically reasonable model for compact star whose energy density of the order $10^{15}~\mbox{g}/\mbox{cm}^{3}$ . Using the Tolman-Oppenheimer-Volkoff equations, we explore the hydrostatic equilibrium and the stability of the compact stars like PSR J1614-2230, 4U 1608-52, SAX J1808.4-3658, LMC X-4, RX J1856-37, Vela X-1, 4U 1820-30, EXO 1785-248, PSR J1903+327, 4U 1538-52, SMC X-1, Her X-1 and Cen X-3. We also estimated the mass and radius of such compact stars.

General relativistic model for mixed fluid sphere with equation of state

We generate a general frame work to solve the Einstein system with an equation of state that describe static spherically symmetric anisotropic matter distribution in terms of a generating function. It is examined for a Van der Waals type equation of state with a physically reasonable form of generating function. The model satisfies all the required major physical properties of a realistic star. It is shown to be stable in the low-density regime that may represent a liquid–gas mixed fluid sphere.

Analytical Models for Quark Stars with Van Der Waals Modified Equation of State

Stellar models consisting of spherically symmetric distribution of charged matter locally anisotropic in strong gravitational fields have been widely considered in the frame of general relativity. These investigations require the generation of exact models through the resolution of the Einstein-Maxwell system of equations. The presence of charge produces values for redshifts, luminosity and mass for the stars different in relation to neutral matter. Some applications for dense charged matter we have them in the description of quark stars, spheres with linear or non-linear equation of state, hybrid stars and accreting process in compact objects where the matter acquires large amounts of electric charge. In this paper, we studied the behavior of relativistic compact objects with anisotropic matter distribution considering Van der Waals modified equation of state proposed in 2013 for Malaver and a gravitational potential Z(x) that depends on an adjustable parameter α in order to integrate analytically the field equations. They generalize the ideal gas law based on plausible reasons that real gases do not act ideally. New exact solutions of the Einstein-Maxwell system are generated and the physical variables as the energy density, radial pressure, mass function, anisotropy factor and the metric functions are written in terms of elementary and polynomial functions. We obtained expressions for radial pressure, density and mass of the stellar object physically acceptable with two different values of the adjustable parameter. The proposed models satisfy all physical features of a realistic star.

Galaxies flowing in the oriented saddle frame of the cosmic web

The strikingly anisotropic large-scale distribution of matter made of an extended network of voids delimited by sheets, themselves segmented by filaments, within which matter flows towards compact nodes where they intersect, imprints its geometry on the dynamics of cosmic flows, ultimately shaping the distribution of galaxies and the redshift evolution of their properties. The (filament-type) saddle points of this cosmic web provide a local frame in which to quantify the induced physical and morphological evolution of galaxies on large scales. The properties of virtual galaxies within the Horizon-AGN simulation are stacked in such a frame. The iso-contours of the galactic number density, mass, specific star formation rate (sSFR), kinematics and age are clearly aligned with the filament axis with steep gradients perpendicular to the filaments. A comparison to a simulation without feedback from active galactic nuclei (AGN) illustrates its impact on quenching star formation of centrals away from the saddles. The redshift evolution of the properties of galaxies and their age distribution are consistent with the geometry of the bulk flow within that frame. They compare well with expectations from constrained Gaussian random fields and the scaling with the mass of non-linearity, modulo the redshift dependent impact of feedback processes. Physical properties such as sSFR and kinematics seem not to depend only on mean halo mass and density: the residuals trace the geometry of the saddle, which could point to other environment-sensitive physical processes, such as spin advection, and AGN feedback at high mass.

Convection and cracking stability of spheres in general relativity

In the present paper we consider convection and cracking instabilities as well as their interplay. We develop a simple criterion to identify equations of state unstable to convection, and explore the influence of buoyancy on cracking (or overturning) for isotropic and anisotropic relativistic spheres. We show that a density profile rho (r), monotonous, decreasing and concave , i.e. rho ' < 0 and rho '' < 0, will be stable against convection, if the radial sound velocity monotonically decreases outward. We also studied the cracking instability scenarios and found that isotropic models can be unstable, when the reaction of the pressure gradient is neglected, i.e. delta mathcal {R}_p = 0; but if it is considered, the instabilities may vanish and this result is valid, for both isotropic and anisotropic matter distributions.

Exact solution of anisotropic compact stars via mass function

The interest in studying relativistic compact objects play an important role in modern astrophysics with an aim to understand several astrophysical issues. It is therefore natural to ask for internal structure and physical properties of specific classes of compact star for astrophysical observable, and we obtain a class of new relativistic solutions with anisotropic distribution of matter for compact stars. More specifically, stellar models, described by the anisotropic fluid, establish a relation between metric potentials and generating a specific form of mass function are explicitly constructed within the framework of General Relativity. New solutions that can be used to model compact objects which adequately describe compact strange star candidates like SMC X-1, Her X-1 and 4U 1538-52, with observational data taken from Gangopadhyay et al. [1]. As a possible astrophysical application the obtained solution could explain the physics of self-gravitating objects, might be useful for strong-field regimes where data are currently inadequate.

Dynamical instability of spherical anisotropic sources in $\mathrm{ f(R,T,R_{\mu\nu}T^{\mu\nu})}$ f ( R , T , R μ ν T μ ν ) gravity

In this paper, we study the effects of modification of gravity on the problem of dynamical instability of the spherical relativistic anisotropic interiors. We have considered non-zero influence of expansion scalar throughout during the evolutionary phases of spherical geometry that led to the use of fluid stiffness parameter. The modified hydrostatic equation for the stellar anisotropic matter distributions is constructed and then solved by using radial perturbation scheme. Such a differential equation can be further used to obtain instability constraints at both weak field and post-Newtonian approximations after considering a particular Harrison-Wheeler equation of state. This approach allows us to deal with the effects of usual and effective matter variables on the stability exotic stellar of self-gravitating structures.

Effects of charge on dynamical instability of spherical collapse in f(R, T) gravity

The effects of charge on stable structure of spherically symmetric collapsing model comprising anisotropic matter distribution are studied in f(R, T) gravity, where R and T correspond to scalar curvature and trace of the energy-momentum tensor, respectively. We construct the field equations, Maxwell equations and dynamical equations in this scenario. We employ linear perturbation scheme on physical variables, metric functions as well as modified terms to establish the evolution or collapse equation for a consistent functional form of f(R, T) gravity. We investigate the limit of instability in Newtonian as well as post Newtonian regimes. It is found that charge plays a fundamental role to slow down the collapse and form a more stable system.

Anisotropic strange stars in the Einstein\u2013Maxwell spacetime

We present here a detailed analysis on the effects of charge on the anisotropic strange star candidates by considering a spherically symmetric interior spacetime metric. To obtain exact solution of the Einstein–Maxwell field equations we have considered the anisotropic strange quark matter (SQM) distribution governed by the simplified MIT bag equation of state (EOS), p=frac{1}{3}left( {rho }-4,B right) , where B is the bag constant and the distribution of the electrical charge is given as q(r)=Qleft( {r}/{R}right) ^3=alpha {r^3}, where alpha is a constant. To calculate different constants we have described the exterior spacetime by the Reissner-Nordström metric. By using the values of the observed mass for the different strange star candidates we have maximized anisotropic stress at the surface to predict the exact values of the radius for the different values of alpha and a specific value of the bag constant. Further, we perform different tests to study the physical validity and the stability of the proposed stellar model. We found accumulation of the electric charge distribution is maximum at the surface having electric charge of the order {{10}^{20}}~C and electric field of the order {10}^{21-22} V/cm.

Relativistic compact stars with charged anisotropic matter

In this article, we perform a detailed theoretical analysis of new exact solutions with anisotropic fluid distribution of matter for compact objects subject to hydrostatic equilibrium. We present a family solution to the Einstein-Maxwell equations describing a spherically symmetric, static distribution of a fluid with pressure anisotropy. We implement an embedding class one condition to obtain a relation between the metric functions. We generalize the properties of a spherical star with hydrostatic equilibrium using the generalised Tolman-Oppenheimer-Volkoff (TOV) equation. We match the interior solution to an exterior Reissner-Nordström one, and study the energy conditions, speed of sound, and mass-radius relation of the star. We also show that the obtained solutions are compatible with observational data for the compact object Her X-1. Regarding our results, the physical behaviour of the present model may serve for the modeling of ultra compact objects.

Existence of compact structures in f(R,\xa0T) gravity

The present paper is devoted to investigate the possible emergence of relativistic compact stellar objects through modified f(R, T) gravity. For anisotropic matter distribution, we used Krori and Barura solutions and two notable and viable f(R, T) gravity formulations. By choosing particular observational data, we determine the values of constant in solutions for three relativistic compact star candidates. We have presented some physical behavior of these relativistic compact stellar objects and some aspects like energy density, radial as well as transverse pressure, their evolution, stability, Eos parameters, measure of anisotropy and energy conditions.

New anisotropic fluid spheres from embedding

The embedding of the manifold into a 5-dimensional flat spacetime leads to a relationship between the gravitational metric potentials. The embedding condition is solved to obtain a new exact solution for an anisotropic matter distribution. We show that the potentials are well behaved, the matter variables have realistic profiles and the solution can be utilized to construct relativistic compact fluid spheres. A detailed investigation of the astrophysical objects 4U 1538-52, Her X-1 and SAX J1808.4-3658 is undertaken. The predicted radii generated through the observed masses for our models are consistent with the above astrophysical objects and indicate that the new exact solution represents compact spheres. The study reveals that complicated geometries arise from embedding and they are physically relevant in the study of observed compact bodies.

Exact anisotropic polytropic cylindrical solutions

In this paper, we study anisotropic compact stars with static cylindrically symmetric anisotropic matter distribution satisfying polytropic equation of state. We formulate the field equations as well as the corresponding mass function for the particular form of gravitational potential $z(x)=(1+bx)^{\eta }~(\eta =1,~2,~3)$ and explore exact solutions of the field equations for different values of the polytropic index. The values of arbitrary constants are determined by taking mass and radius of compact star (Her X-1). We find that resulting solutions show viable behavior of physical parameters (density, radial as well as tangential pressure, anisotropy) and satisfy the stability condition. It is concluded that physically acceptable solutions exist only for $\eta =1,~2$ .

Anisotropic charged physical models with generalized polytropic equation of state

In this paper, we found the exact solutions of Einstein–Maxwell equations with generalized polytropic equation of state (GPEoS). For this, we consider spherically symmetric object with charged anisotropic matter distribution. We rewrite the field equations into simple form through transformation introduced by Durgapal (Phys Rev D 27:328, 1983) and solve these equations analytically. For the physically acceptability of these solutions, we plot physical quantities like energy density, anisotropy, speed of sound, tangential and radial pressure. We found that all solutions fulfill the required physical conditions. It is concluded that all our results are reduced to the case of anisotropic charged matter distribution with linear, quadratic as well as polytropic equation of state.

Anisotropic extension of Finch and Skea stellar model

In this paper, the spacetime geometry of Finch and Skea [Class. Quantum Grav., 6 (1989) 467] has been utilized to obtain closed-form solutions for a spherically symmetric anisotropic matter distribution. By examining its physical admissibility, it has been shown that the class of solutions can be used as viable models for observed pulsars. In particular, a specific class of solutions can be used as an `anisotropic switch' to examine the impact of anisotropy on the gross physical properties of a stellar configuration. Accordingly, the mass-radius relationship has been analyzed.