Anisotropic Matter Distribution Research Articles

Cracking isotropic and anisotropic relativistic spheres

We explore the influence of density fluctuations on isotropic and anisotropic configurations, extending the concept of cracking for isotropic general relativistic fluid spheres. This concept, conceived to describe the behaviour of anisotropic matter distributions just after its departure from equilibrium, could provide some insight on potential instabilities and future evolution of relativistic fluids. We have refined the idea of cracking, considering local fluctuations—represented by any function of compact support defined in a closed interval—and their effect on the state variables and gradients through “barotropic” equations of state, P = P(ρ) and [Formula: see text]. Under this approach it is found that both isotropic and anisotropic models could exhibit cracking (or overturning), and that previous results for cracking (and overturning) instabilities on anisotropic matter configurations has to be revised.

Emerging anisotropic compact stars in f(mathcal {G},T) gravity

The possible emergence of compact stars has been investigated in the recently introduced modified Gauss–Bonnet f(mathcal {G},T) gravity, where mathcal {G} is the Gauss–Bonnet term and T is the trace of the energy-momentum tensor (Sharif and Ikram, Eur Phys J C 76:640, 2016). Specifically, for this modified f(mathcal {G}, T) theory, the analytic solutions of Krori and Barua have been applied to an anisotropic matter distribution. To determine the unknown constants appearing in the Krori and Barua metric, the well-known three models of the compact stars, namely 4U1820-30, Her X-I, and SAX J 1808.4-3658 have been used. The analysis of the physical behaviour of the compact stars has been presented and the physical features like energy density and pressure, energy conditions, static equilibrium, stability, measure of anisotropy, and regularity of the compact stars, have been discussed.

Conformally non-flat spacetime representing dense compact objects

A new conformally non-flat interior spacetime embedded in five-dimensional (5D) pseudo Euclidean space is explored in this paper. We proceed our calculation with the assumption of spherically symmetric anisotropic matter distribution and Karmarkar condition (necessary condition for class one). This solution is free from geometrical singularity and well-behaved in all respects. We ansatz a new type of metric potential [Formula: see text] and solve for the metric potential [Formula: see text] via Karmarkar condition. Further, all the physical parameters are determined from Einstein’s field equations using the two metric potentials. All the constants of integration are determined using boundary conditions. Due to its conformally non-flat character, it can represent bounded configurations. Therefore, we have used it to model two compact stars Vela X-1 and Cyg X-2. Indeed, the obtained masses and radii of these two objects from our solution are well matched with those observed values given in [T. Gangopadhyay et al., Mon. Not. R. Astron. Soc. 431, 3216 (2013)] and [J. Casares et al., Mon. Not. R. Astron. Soc. 401, 2517 (2010)]. The equilibrium of the models is investigated from generalized TOV-equation. We have adopted [L. Herrera’s, Phys. Lett. A 165, 206 (1992)] method and static stability criterion of Harisson–Zeldovich–Novikov [B. K. Harrison et al., Gravitational Theory and Gravitational Collapse (University of Chicago Press, 1965); Ya. B. Zeldovich and I. D. Novikov, Relativistic Astrophysics, Vol. 1, Stars and Relativity (University of Chicago Press, 1971)] to analyze the stability of the models.

Relativistic modeling of compact stars for anisotropic matter distribution

In this paper we have solved Einstein's field equations of spherically symmetric spacetime for anisotropic matter distribution by assuming physically valid expressions of the metric function $e^{\lambda}$ and radial pressure ( $p_{r}$ ). Next we have discussed the physical properties of the model in details by taking the radial pressure $p_{r}$ equal to zero at the boundary of the star. The physical analysis of the star indicates that its model parameters such as density, redshift, radial pressure, transverse pressure and anisotropy are well behaved. Also we have obtained the mass and radius of our compact star which are $2.29M_{\odot}$ and 11.02 km, respectively. It is observed that the model obtained here for compact stars is compatible with the mass and radius of the strange star PSR 1937 +21 .

A new class of relativistic model of compact stars of embedding class I

In the present paper, we have constructed a new relativistic anisotropic compact star model having a spherically symmetric metric of embedding class one. Here we have assumed an arbitrary form of metric function [Formula: see text] and solved the Einstein’s relativistic field equations with the help of Karmarkar condition for an anisotropic matter distribution. The physical properties of our model such as pressure, density, mass function, surface red-shift, gravitational redshift are investigated and the stability of the stellar configuration is discussed in details. Our model is free from central singularities and satisfies all energy conditions. The model we present here satisfy the static stability criterion, i.e. [Formula: see text] for [Formula: see text][Formula: see text]g/cm3(stable region) and for [Formula: see text][Formula: see text]g/cm3, the region is unstable i.e. [Formula: see text].

Detection prospects for high energy neutrino sources from the anisotropic matter distribution in the local Universe

Constraints on the number and luminosity of the sources of the cosmic neutrinos detected by IceCube have been set by targeted searches for point sources. We set complementary constraints by using the 2MASS Redshift Survey (2MRS) catalogue, which maps the matter distribution of the local Universe. Assuming that the distribution of the neutrino sources follows that of matter, we look for correlations between ``warm'' spots on the IceCube skymap and the 2MRS matter distribution. Through Monte Carlo simulations of the expected number of neutrino multiplets and careful modelling of the detector performance (including that of IceCube-Gen2), we demonstrate that sources with local density exceeding 10−6 Mpc−3 and neutrino luminosity Lν ≲ 1042 erg s−1 (1041 erg s−1) will be efficiently revealed by our method using IceCube (IceCube-Gen2). At low luminosities such as will be probed by IceCube-Gen2, the sensitivity of this analysis is superior to requiring statistically significant direct observation of a point source.

Spherical relativistic vacuum core models in a $\Lambda$ Λ -dominated era

This paper is devoted to analyzing the effects of the cosmological constant in the evolution of exact analytical collapsing vacuum core celestial models. For this purpose, relativistic spherical geometry coupled with null expansion locally anisotropic matter distributions is considered. We have first developed a relation between tidal forces and structural variables. We then explored some viable spherical cosmological models by taking the expansion-free condition. Our first class of spherical models is obtained after constraining system matter content, while the second class is obtained by considering barotropic equation of state. We propose that our calculated solutions could be regarded as a relativistic toy model for those astronomical compact populations where vacuum core is expected to appear, like cosmological voids.

A realistic model for charged strange quark stars

We report a general approach to solve an Einstein-Maxwell system to describe a static spherically symmetric anisotropic strange matter distribution with linear equation of state in terms of two generating functions. It is examined by choosing Tolmann IV type potential for one of the gravitational potentials and a physically reasonable choice for the electric field. Hence, the generated model satisfies all the required major physical properties of a realistic star. The effect of electric charge on physical properties is highlighted.

Anisotropic compact stars in Karmarkar spacetime

We present a new class of solutions to the Einstein field equations for an anisotropic matter distribution in which the interior space-time obeys the Karmarkar condition. The necessary and sufficient condition required for a spherically symmetric space-time to be of Class One reduces the gravitational behavior of the model to a single metric function. By assuming a physically viable form for the grr metric potential we obtain an exact solution of the Einstein field equations which is free from any singularities and satisfies all the physical criteria. We use this solution to predict the masses and radii of well-known compact objects such as Cen X-3, PSR J0348+0432, PSR B0943+10 and XTE J1739-285.

Shear-free stellar solutions in $\Lambda$ Λ -dominated era

The exact analytical collapsing solutions have been explored under the effects of cosmological constant with shear-free condition. We have considered the geometry to be spherically symmetric, which is filled with anisotropic matter distribution. An explicit link has been constructed between the inhomogeneous forces with material profile. The Darmois matching conditions are explored by assuming suitable geometry as an exterior spacetime. We continued our investigation of exact solutions in two different scenarios. The first one is done by restraining the mass function as a main ingredient while the second one includes particular restrictions on the matter profile and equation of state. We found that some of the obtained solutions satisfy the Darmois matching conditions.

Modelling of anisotropic compact stars of embedding class one

In the present article, we have constructed static anisotropic compact star models of Einstein field equations for the spherical symmetric metric of embedding class one. By assuming the particular form of metric function $\nu$, We have solved the Einstein field equations for anisotropic matter distribution. The anisotropic models are representing the realistic compact objects such as SAX J 1808.4-3658 (SS1), Her X - 1, Vela X-12, PSR J1614-2230 and Cen X - 3. We have reported our results in details for compact star Her X-1 on the ground of physical properties such as pressure, density, velocity of sound, energy conditions, TOV equation and red-shift etc. Along with these, we have also discussed about stability of the compact star models. Finally we made the comparison between our anisotropic stars with the realistic objects on the key aspects as central density, central pressure, compactness and surface red-shift.

Relativistic compact anisotropic charged stellar models with Chaplygin equation of state

This paper presents a new model of static spherically symmetric relativistic charged stellar objects with locally anisotropic matter distribution together with the Chaplygin equation of state. The interior spacetime has been matched continuously to the exterior Reissner–Nordstrom geometry. Different physical properties of the stellar model have been investigated, analyzed, and presented graphically.

Charged cylindrical polytropes with generalized polytropic equation of state

We study the general formalism of polytropes in relativistic regime with generalized polytropic equations of state in the vicinity of cylindrical symmetry. We take charged anisotropic fluid distribution of matter with conformally flat condition for the development of general framework of polytropes. We discussed the stability of the model by Whittaker formula and concluded that one of the developed model is physically viable.

Static spherically symmetric solutions in f(G) gravity

We investigate interior solutions for static spherically symmetric metric in the background of [Formula: see text] gravity. We use the technique of conformal Killing motions to solve the field equations with both isotropic and anisotropic matter distributions. These solutions are then used to obtain density, radial and tangential pressures for power-law [Formula: see text] model. For anisotropic case, we assume a linear equation-of-state and investigate solutions for the equation-of-state parameter [Formula: see text]. We check physical validity of the solutions through energy conditions and also examine its stability. Finally, we study equilibrium configuration using Tolman–Oppenheimer–Volkoff equation.

Anisotropic generalization of Matese & Whitman solution for compact star models in general relativity

We present a detailed investigation of the stability of anisotropic compact star models by introducing Matese and Whitman (Phys. Rev. D 11:1270, 1980) solution in general relativity. We have particularly looked into the detailed investigation of the measurements of basic physical parameters such as radial pressure, tangential pressure, energy density, red shift, sound velocity, masses and radii are affected by unknown effects such as loss, accretion and diffusion of mass. Those give insight into the characteristics of the compact astrophysical object with anisotropic matter distribution as well as the physical reality. The results obtained for the physical feature of compact stars such as, Her. X-1, RXJ 1856-37, SAX J1808.4-3658(SS2) and SAX J1808.4-3658(SS1) are compared to the recently observed massive compact object.

Anisotropic star on pseudo-spheroidal spacetime

A new class of exact solutions of Einstein's field equations representing anisotropic distribution of matter on pseudo-spheroidal spacetime is obtained. The parameters appearing in the model are restricted through physical requirements of the model. It is found that the models given in the present work is compatible with observational data of a wide variety of compact objects like 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, PSR J1614-2230, SMC X-4, Cen X-3. A particular model of pulsar PSR J1614-2230 is studied in detail and found that it satisfies all physical requirements needed for physically acceptable model.

Conformally flat polytropes for anisotropic cylindrical geometry

In this paper, we study cylindrically symmetric anisotropic matter distribution satisfying two polytropic equations of state. The corresponding Lane–Emden equations are constructed and the energy conditions are checked. We evaluate a particular expression for anisotropy by using the conformally flat condition, which helps in the study of polytropic models. The graphical analysis of surface gravitational potential indicates the increasing behavior of model compactness. Finally, we conclude that one of the obtained models is physically viable.

Compact stars on pseudo-spheroidal spacetime compatible with observational data

A new class of solutions for Einstein's field equations representing a static spherically symmetric anisotropic distribution of matter is obtained on the background of pseudo-spheroidal spacetime. We have prescribed the bounds of the model parameters $ k $ and $ p_0 $ on the basis of the elementary criteria for physical acceptability, viz., regularity, stability and energy conditions. By taking the values of model parameters from the prescribed bounds, we have shown that our model is compatible with the observational data of a wide variety of compact stars like 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, PSR J1614-2230, SMC X-4 and Cen X-3.

The Finslerian compact star model

We construct a toy model for compact stars based on the Finslerian structure of spacetime. By assuming a particular mass function, we find an exact solution of the Finsler-Einstein field equations with an anisotropic matter distribution. The solutions are revealed to be physically interesting and pertinent for the explanation of compact stars.

Effects of charge on anisotropic conformally flat polytropes

In this paper, we study the effects of electromagnetic field on conformally flat spherically symmetric anisotropic matter distribution satisfying two polytropic equations of state. We consider conformally flat condition and evaluate corresponding anisotropy, which is used to study polytropes for the charged compact object. Finally, we study stability of the resulting models using the Tolman mass. It is concluded that only one of the resulting models is physically viable.