Static fluid spheres in Einstein-Cartan theory

Following the work of Trautman we have described briefly the Einstein-Cartan equations with special reference to a perfect fluid distribution and then obtained three solutions adopting Hehl's approach and Tolman's technique. We have found that a space-time metric similar to the Schwarzschild solution (interior) will no longer represent a homogeneous fluid sphere in the presence of spin density, and the corresponding equation of state has the form $8\pi p=8\mathrm{}\pi \rho -\frac{6}{R^2}+\left(\frac{B_2}{2\pi A{R}^2}\right){(8\mathrm{}\pi \rho -\frac{3}{R^2})}^{\frac{1}{2}}$, where $R$, $B_2$, and $A$ are constants. At the boundary of the fluid sphere the hydrostatic pressure $p$ is discontinuous.