Static spherical configurations of cold matter in the Einstein-Cartan theory of gravitation

Abstract

We investigate static, spherical configurations of cold catalized matter in the Einstein-Cartan theory of gravitation. Assuming that density of spin is proportional to the number density of baryonsn and using an equation of state of a degenerate, relativistic Fermi gas, we numerically integrated the relativistic equation of equilibrium. We have also studied the stability of those configurations. Configurations with central number densityn _c such that$d\tilde p|dn|_{n = n_c } > 0$ where$\tilde p$ is the effective pressure, are very similar to general relativistic configurations with the same central density. In the Einstein-Cartan theory there exists another disjoint family of equilibrium configurations for which$d\tilde p|dn|_{n = n_c }< 0$ but$\tilde p(n = n_c ) > 0$. Those configurations have very small masses ∼10⁻⁶ g and raddi ∼10⁻³⁴ cm and are unstable.