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 We have found that a space-time metric similar to the Schwarzschild solution (interior) will no longer represent a homogeneous fluid sphere in the presence of spin density, and the corresponding equation of state has the form $8{π}p=8{π}{ρ}{-}{6}{{R}²}+({{B}₂}{2{π}A{R}²}){(8{π}{ρ}{-}{3}{{R}²})}1/2$, where $R$, ${B}₂$, and $A$ are constants. At the boundary of the fluid sphere the hydrostatic pressure $p$ is discontinuous.