Solutions of Einstein's field equations for static fluid spheres

Five new analytic solutions are presented. One of them has the equation of state $P=K_0{\rho }^{1+\frac{1}{n}}+{\sigma }_1\rho$, where ${\sigma }_1=\frac{P_c}{{\rho }_c{c}^2}$ and $K_0$ and $n$ are constants; both pressure and density diverge at the origin while their ratio remains finite. Since the second term could be negligible at high densities, this solution can be considered as an analog of a relativistic polytrope over a certain range of radius. Each solution has been considered in some detail.