Static Weyssenhoff Fluid Sphere Models in Einstein–Cartan Theory of Gravitation

Three physically reasonable static Weyssenhoff fluid sphere models have been obtained by solving the relevant field equations of the Einstein–Cartan theory of gravitation, when Weyssenhoff fluid is the source of spin and gravitation. The spin of the gravitating matter influences the fields of these fluid sphere models. The gravitational field of two of the models is proved to be of Petrov type \(D\), while the interpretation of the gravitational field of the remaining model fails due to the influence of the spin component \(s_{0}\). One of the fluid sphere models is accelerating and rotating, while the other two are only rotating. Gravity in each of these models repels and prevents the collapse.