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.     

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.     

Varieties of new classes of interior solutions in general relativity

In this paper we present a method of obtaining varieties of new classes of exact solutions representing static balls of perfect fluid in general relativity. A number of previously known classes of solutions has been rediscovered in the process. The method indicates the possibility of constructing a plethora of new physically significant models of relativistic stellar interiors with equations of state fairly applicable to the case of extremely compressed stars. To emphasize our point we have derived two new classes of solutions and discussed their physical importance. From the solutions of these classes we have constructed three causal interiors out of which in two models the outward march of pressure, density, pressure-density ratio and the adiabatic sound speed is monotonically decreasing.     

A new well behaved exact solution in general relativity for perfect fluid

We present a new spherically symmetric solution of the general relativistic field equations in isotropic coordinates. The solution is having positive finite central pressure and positive finite central density. The ratio of pressure and density is less than one and casualty condition is obeyed at the centre. Further, the outmarch of pressure, density and pressure-density ratio, and the ratio of sound speed to light is monotonically decreasing. The solution is well behaved for all the values of u lying in the range 0<u≤.186. The central red shift and surface red shift are positive and monotonically decreasing. Further, we have constructed a neutron star model with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. The maximum mass of the Neutron star comes out to be M=1.591 M _Θ with radius R _b ≈12.685 km. The most striking feature of the solution is that the solution not only well behaved but also having one of the simplest expressions so far known well behaved solutions. Moreover, the good matching of our results for Vela pulsars show the robustness of our model.     

Viscous fluid universe filled with stiff fluid in general relativity

We have investigated two stiff-fluid models in which the material distribution is that of viscous fluid. In the first model, the coefficient of shear viscosity is assumed to be constant while in the second model the coefficient of shear viscosity is proportional to the rate of expansion in the model. The paper also discusses some physical and geometrical aspects of the model. The behaviour of the model in absence of viscosity is also discussed.     

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.     

Anisotropic Bianchi type-I models with constant deceleration parameter in general relativity

A special law of variation for Hubble’s parameter is presented in a spatially homogeneous and anisotropic Bianchi type-I space-time that yields a constant value of deceleration parameter. Using the law of variation for Hubble’s parameter, exact solutions of Einstein’s field equations are obtained for Bianchi-I space-time filled with perfect fluid in two different cases where the universe exhibits power-law and exponential expansion. It is found that the solutions are consistent with the recent observations of type Ia supernovae. A detailed study of physical and kinematical properties of the models is carried out.     

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.     

An inhomogeneous stiff fluid universe with electromagnetic field in general relativity

An inhomogeneous cylindrically symmetric cosmological model for stiff perfect fluid distribution with electromagnetic field is obtained.F ₁₂ is the non-vanishing component of electromagnetic field tensor. The metric potentials are functions ofx andt both. The behaviour of the electromagnetic field tensor together with geometrical and physical aspects of the model are also examined.     

Inhomogeneous viscous fluid cosmological model with electromagnetic field in general relativity

The object of this paper is to investigate the behaviour of electromagnetic field in inhomogeneous cosmological models obtained for viscous fluid distributions. The various particular cases when both the electromagnetic and viscosity are absent, are also discussed.     

Charged fluid sphere in bimetric general theory of relativity

Static and spherical symmetric solutions of the field equations in the bimetric general theory of gravitation are obtained for perfect and anisotropic charged fluids under the assumption that the physical metric admits a one-parameter group of conformal motion. All solutions are matched to the Reissner–Nordstrom metric and possess positive energy density larger than the stresses, everywhere within the sphere. The solution agrees with Einstein’s general relativity for a physical system comparable to the size of the universe, such as the solar system.     

Uniform radial motion of sound in a relativistic fluid ball

We present a new class of spherically symmetric exact solutions of the general relativistic field equations. These solutions describe perfect fluid balls with infinite central pressure and central density though their ratio is finite. A member of the class has been studied in detail from which we have constructed a model of causal fluid ball with constant sound speed.     

Expanding and shearing magneto-viscous fluid cosmological model in general relativity

The object of this paper is to investigate the behavior of a magnetic field in a viscous fluid cosmological model. It has been assumed that the expansion () is proportional to the eigenvalue ₁ of the shear tensor _i ^j and the coefficient of shearing viscosity is proportional to the scalar of expansion. The paper also discusses the behavior of the model when the magnetic field tends to zero and comments on some other physical properties.     

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.     

Magneto-viscous fluid cosmological model of plane symmetry in general relativity

The object of this paper is to investigate the behaviour of magnetic field in a viscous fluid cosmological model. Various physical and geometrical properties of the model have also been discussed.     

Anisotropic fluid distribution in higher dimensional general theory of relativity

We have obtained static and spherically symmetric self-gravitating solution of the field equations for anisotropic distribution of matter in higher- dimensional in the context of Einstein’s general theory of relativity. This work is an extension of the previous work of Hector Rago (Astrophys. Space Sci. 183:333, 1991) for four dimensional space-time. The solutions are matched to the analytical solutions for spherically symmetric self gravitating distribution of anisotropic matter obtained by Hector Rago (1991) for n=2.     

Some expanding and shearing viscous fluid cosmological models in general relativity

Two cylindrically-symmetric cosmological models representing viscous fluid distributions when free-gravitational field of typeD where coefficient of shear viscosity is assumed to be proportional to the rate of expansion, are obtained. The behaviour of the models in the absence of viscosity and other physical properties are also discussed.     

A gravitationally non-degenerate cosmological model with expanding and shearing viscous fluid in general relativity

The object of this paper is to investigate the behaviour of viscosity in a cosmological model, in which the coefficient of shear viscosity is assumed to be proportional to rate of expansion in the model. The behaviour of the model in the absence of shear viscosity is also discussed.