Anisotropic spheres with variable energy density in general relativity

Interior solutions of Einstein field equations for anisotropic spheres with variable energy density are obtained. The solutions for uniform energy density [10] and for radial pressure equal to zero [11] are particular cases of the present solution. With this solution we are also able to discuss an anisotropic gas sphere. Physically it explains larger red-shifts of different quasi-stellar objects. The results of the model have been used to explain the behaviour of a neutron stars and conclude that the maximum mass of a neutron star does not exceed two solar masses, which confirms the Chandrasekhar limit.