A class of charged relativistic spheres

We find a new class of exact solutions to the Einstein-Maxwell equations which can be used to model the interior of charged relativistic objects. These solutions can be written in terms of special functions in general; for particular parameter values it is possible to find solutions in terms of elementary functions. Our results contain models found previously for uncharged neutron stars and charged isotropic spheres.Comment: 11 pages, To appear in Mathematical and Computational Application

Some new static anisotropic spheres

In recent years, a number of authors have found solutions to the Einstein field equations for static gravitational fields with anisotropic matter. The models generated are used to describe relativistic spheres with strong gravitational fields. It is for this reason that many investigators use a variety of techniques to attain exact solutions. The exact solutions may be used to study the physical features of charged spheroidal stars. I found a new class of exact solutions to the Einstein field equation for an anisotropic sphere with the particular choice of the anisotropic factor A= pc — pr, the difference between the radial and the tangential pressures of the fluid sphere and one of the gravitational potential Z. The condition of pressure anisotropy was reduced to a recurrence equation with variable, rational coefficients which can be solved in general. Consequently the exact solutions to the Einstein field equations corresponding to a static spherically symmetric gravitational potential was found in terms of series. I generated two linearly independent solutions by placing restriction on parameters arising in the general series. Some brief comments relating to the physical features of the model are also made

Classes of exact isotropic solutions, a solution generating algorithm

Exact solutions of the Einstein-Maxwell field equations are of crucial importance in relativistic astrophysics. These solutions may be utilized to model a charged relativistic star as they are watchable to the Reissner-Nordstrom exterior at the boundary. In order to solve the field equations, various restrictions have been placed on the geometry of space time and the matter content. Mainly two distinct procedures have been adopted to solve these equations. Firstly, the coupled differential equations are solved by computation after choosing an equation of state. Secondly, the exact Einstein-Maxwell solutions can be obtained by specifying the geometry and the form of the electric field. In this paper, I used the latter technique to establish a new algorithm that generates a new solution to the Einstein-Maxwell field equations from a seed solution. The new solution is expressed in terms of integral of known functions, and the integration can be completed in principle. The applicability of this technique has already been demonstrated by generating new solution for a seed solutio

Exact models for anisotropic fluid sphere

Two categories of exact solutions are found to the Einstein field equations for an anisotropic fluid sphere with a particular choice of the anisotropic factor and one of the gravitational potentials. The condition of pressure isotropy is reduced to alinearsecond order differential equationwhich can be solved in general.Consequentlywe can find exact solutions to the Einstein field equations correspondingto a static spherically symmetric gravitational potential in terms of elementaryfunctions, namely polynomials and product of polynomials andalgebraic functions.These solutions contain particular solutions found previously includingmodels of isotropic relativistic sphere

Anisotropic spheroidal model

Exact solutionto the anisotropic Einstein field equations is obtained with a specified form of the anisotropicfactor. The field equations are transformed to a simpler form; the integration of the system is reduced to solving the condition of pressure anisotropy. It is possible to obtain general class of solutions in terms of elementary functions that model the interior of relativistic fluid sphere

Analytical models for quark stars

We find two new classes of exact solutions to the Einstein-Maxwell system of equations. The matter content satisfies a linear equation of state consistent with quark matter; a particular form of one of the gravitational potentials is specified to generate solutions. The exact solutions can be written in terms of elementary functions, and these can be related to quark matter in the presence of an electromagnetic field. The first class of solutions generalises the Mak and Harko model. The second class of solutions does not admit any singularities in the matter and gravitational potentials at the centre.Comment: 10 pages, To appear in Int. J. Mod. Phys.

Classes of exact Einstein-Maxwell solutions

We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein-Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.Comment: 16 pages, To appear in Gen. Relativ. Gravi