On a family of well behaved perfect fluid balls as astrophysical objects in general relativity

A family of well behaved perfect fluid balls has been derived starting with the metric potential g ₄₄=B(1+Cr ²) ⁿ for all positive integral values of n. For n≥4, the members of this family are seen to satisfy the various physical conditions e.g. c ² ρ≥p≥0,dp/dr<0,dρ/dr<0, along with the velocity of sound \((\sqrt{dp/c^{2}d\rho} )< 1\) and the adiabatic index ((p+c ² ρ)/p)(dp/(c ² dρ))>1. Also the pressure, energy density, velocity of sound and ratio of pressure and energy density are of monotonically decreasing towards the pressure free interface (r=a). The fluid balls join smoothly with the Schwarzschild exterior model at r=a. The well behaved perfect fluid balls so obtained are utilised to construct the superdense star models with their surface density 2×10¹⁴  gm/cm³. We have found that the maximum mass of the fluid balls corresponding to various values of n are decreasing with the increasing values of n. Over all maximum mass for the whole family turns out to be 4.1848M _Θ and the corresponding radius as 19.4144 km while the red shift at the centre and red shift at surface as Z ₀=1.6459 and Z _a =0.6538 respectively this all happens for n=4. It is interesting to note that for higher values of n viz n≥170, the physical data start merging with that of Kuchowicz superdense star models and hence the family of fluid models tends to the Kuchowicz fluid models as n→∞. Consequently the maximum mass of the family of solution can not be less than 1.6096 M _Θ which is the maximum mass occupied by the Kuchowicz superdense ball. Hence each member of the family for n≥4 provides the astrophysical objects like White dwarfs, Quark star, typical neutron star.     

New class of regular and well behaved exact solutions in general relativity

We present a new class of spherically symmetric regular and well behaved solutions of the general relativistic field equations in isotropic coordinates. These solutions describe perfect fluid balls with positively finite central pressure and positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The solutions of this class, the outmarch of pressure, density pressure-density ratio and the ratio of sound speed to light is monotonically decreasing. Keeping in view of well behaved nature in terms of central red shift and surface red shift and by assuming the surface density ρ _b =2×10¹⁴ g/cm³, we constructed a Neutral star model for k=2, resulting into maximum mass ≈6.36M _Θ, linear dimension ≈48.08 km, surface red shift ≈1.132 and central red shift ≈17.1314.     

Robertson-Walker cosmological models with perfect fluid in general relativity

Einstein's field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for a Robertson-Walker universe by assuming the cosmological term to be proportional to R-m(R is a scale factor and m is a constant).A variety of solutions is presented.The physical significance of the cosmological models has also been discussed.     

A static axisymmetric anisotropic fluid solution in general relativity

Einstein's interior field equations in general relativity are considered when spacetime is static and axisymmetric and the energy-momentum tensor represents an anisotropic fluid. After imposing a set of simplifying assumptions a two-parameter solution is derived and its properties are discussed. The solution is found to be physically reasonable in a certain range of the parameters in which case the metric could represent a core of anisotropic matter.     

Bianchi type-I cosmological models with perfect fluid in general relativity

Einstein's field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-Ⅰ universe by assuming that the cosmological term is proportional to R-m(R is a scale factor and m is a constant).A variety of solutions are presented.The physical significance of the respective cosmological models are also discussed.     

Variety of Well behaved parametric classes of relativistic charged fluid spheres in general relativity

The paper presents a variety of classes of interior solutions of Einstein–Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid with well behaved nature. These classes of solutions describe perfect fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the center. The outmarch of pressure, density, pressure–density ratio and the adiabatic speed of sound is monotonically decreasing for these solutions. Keeping in view of well behaved nature of these solutions, two new classes of solutions are being studied extensively. Moreover, these classes of solutions give us wide range of constant K for which the solutions are well behaved hence, suitable for modeling of super dense star. For solution (I₁) the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³ corresponding to K=1.19 and X=0.20, the maximum mass of the star comes out to be 2.5M _Θ with linear dimension 25.29 Km and central redshift 0.2802. It has been observed that with the increase of charge parameter K, the mass of the star also increases. For n=4,5,6,7, the charged solutions are well behaved with their neutral counterparts however, for n=1,2,3, the charged solution are well behaved but their neutral counterparts are not well behaved.     

Rotating perfect fluids in general relativity

The field equations and the equation of motion for perfect fluids in axially-symmetric-cylindrical coordinates are presented. For rigidly rotating perfect fluid with constant pressure, exact solutions are obtained in symmetric case and axially-symmetric case as well.     

Bianchi Type III magnetized massive string cosmological model for perfect fluid distribution in general relativity

Bianchi Type III massive string cosmological model for perfect fluid distribution in the presence of magnetic field, is investigated. It is assumed that the universe is filled with barotropic perfect fluid. We have attempted to investigate Bianchi Type III string cosmological model incorporating perfect fluid with magnetic field. To get the deterministic model in terms of cosmic time, we have assumed that the expansion (θ) in the model is proportional to the shear. We have also assumed that F ₁₂ is the only non-vanishing component of electromagnetic field tensor F _ij . The behaviour of the model in presence and absence of magnetic field together with singularities in these models are also discussed.     

Some cylindrically-symmetric cosmological models in general relativity representing viscous fluid and perfect fluid with heat conduction

The paper considers inhomogeneous space-times admitting a two-parameter group of motions and satisfying Einstein's field equations for viscous fluid and perfect fluid with heat conduction. Some homogenous solutions representing viscous fluid have also been obtained for which the free-gravitational field is of the magnetic type. Various physical and kinematical properties have been discussed.     

Inhomogeneous generalisation of Bianchi type-VIo cosmological model of perfect fluid distribution in general relativity

Einstein's equations have been solved for perfect fluid distribution. The solution obtained may be considered as inhomogeneous generalisation of Bianchi type-VI_o cosmological model.     

Non-static fluid spheres in general relativity

We critically comment upon the paper: The properties of large particles in the zodiacal cloud and in the interstellar medium, and their relation to recent IRAS observations, by F. Hoyle and N. C. Wickramasinghe, which appeared inAstrophysics and Space Science 107 (1984) 224.     

Radiating fluid spheres in general relativity

In this paper Einstein's field equations for spherically-symmetric radiating fluid distributions are discussed and some new exact regular solutions are obtained.     

A tilted Bianchi type-V perfect fluid solution for stiff matter

We present a solution to the Einstein field equations for a massless scalar field in a Bianchi type-V spacetime, which can be interpreted as a solution for a perfect fluid with the equation of state of stiff matter. This solution complements a solution previously given by us for an anisotropic fluid.     

Charged fluid to anisotropic fluid distribution in general relativity

A new class of well behaved anisotropic super-dense stars has been derived with the help of a given class of charged fluid distributions. The anisotropy parameter (or the electric intensity) is zero at the centre and monotonically increasing towards the pressure free interface. All the physical parameter such as energy density, radial pressure, tangential pressure and velocity of sound are monotonically decreasing towards the surface. The maximum mass measures 3.8593 solar mass and the corresponding radius is 21.2573 km for n=1 i.e. N tends to infinity.     

Anisotropic fluid distributions in bimetric general relativity

Static and spherically-symmetric solutions of the field equations in the bimetric theory of gravitation are obtained for isotropic and anisotropic distributions of matter when the physical metric admits a one-parameter group of conformal motions. The solutions agree with Einstein's general relativity for physical systems comparable to the size of the Universe, such as the solar system.     

String fluid cosmological models in general relativity

LRS Bianchi type-I string cosmological models are studied in the frame work of general relativity when the source for the energy momentum tensor is a bulk viscous fluid containing one dimensional strings embedded in electromagnetic field. A barotropic equation of state for the pressure and density is assumed to get determinate solutions of the field equations. The bulk viscosity is assumed to be inversely proportional to the scalar expansion. The physical and kinematical properties of the models are discussed. The effect of viscosity and electromagnetic field on the physical and kinematical properties is also investigated.