Exact models for anisotropic fluid sphere

Abstract

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 spheres