A new analytical solution has been obtained for stellar models by solving Einstein's field equation for the spherically symmetric and static case. The variation of density is smooth and gradual. The density remains positive under all conditions. For all finite pressures the configurations are stable under radial perturbations. For $\frac{\mathrm{dP}}{d\rho }\le 1$, the maximum mass of a neutron-star model is $4.56M_{\odot }$, and the surface and the central red-shifts are 0.787 and 2.673, respectively. For an infinite central pressure the surface red-shift is 1.575 which is greater than that for any other analytical solution with varying density.

• Received 4 June 1982

DOI:https://doi.org/10.1103/PhysRevD.27.328