Exact models for isotropic matter

Abstract

Abstract. We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently we can find an explicit exact solution to the EinsteinMaxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series we show that the series terminate and there exist two linearly independent solutions. Consequently it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.

Charged Analogue of Finch–skea Stars

“…This leads to differential equations that are highly nonlinear and difficult to integrate. Another option, which is pursued here, is to postulate a form for the gravitational potential Z and to choose a form for the electrostatic field E. Our choice for the function Z(x) is contained in the form used by Thirukkanesh and Maharaj [6] and Maharaj and Mkhwanazi [7] which ensures that we regain as a special case models of fluid spheres with uncharged matter distributions analysed previously. The metric function Z(x) is chosen to be of the form…”

General relativistic model for mixed fluid sphere with equation of state

“…Many exact solutions to the field equations have been generated by different approaches with generalized forms for one of the gravitational potentials that does have an equation of state (EoS) (linear [2][3][4][5][6][7], quadratic [8][9][10], polytropic [11][12][13][14][15][16], Van der Waals [17], etc.) and without [18][19][20][21][22][23][24][25] a particular barotropic EoS relating the pressure to the energy density. However, among large number of such work reported over the years, relatively few of these solutions correspond to non-singular metric functions with physically acceptable energy momentum tensor.…”

Charged anisotropic matter with quadratic equation of state

“…For this purpose, a number of models have been discussed [2][3][4][5][6][7][8][9][10][11][12] by considering the relativistic anisotropic fluid. The study with charged matter is presented in [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. A detailed discussion of a compact relativistic body in the presence of electromagnetic field is given by Thirukkanesh and Maharaj [1].…”