Static fluid spheres in Einstein-Cartan theory

Abstract

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 We have found that a space-time metric similar to the Schwarzschild solution (interior) will no longer represent a homogeneous fluid sphere in the presence of spin density, and the corresponding equation of state has the form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