Isotropic Spherically Symmetric Weyssenhoff Fluid Sphere Models in Einstein–Cartan Theory

We present new exact solutions to the Einstein–Cartan (EC) field equations for static, spherically symmetric configurations of a noncharged Weyssenhoff fluid in isotropic coordinates, derived using the extended technique of differential forms applied to the non-Riemannian space-time of the Einstein–Cartan theory of gravitation (ECTG). The solutions exhibit regular behavior with nonnegative pressure and energy density, and satisfy the adiabatic stability condition $${1/\sqrt{3}<a<1}$$ . All models are rotating and accelerating, with vanishing expansion and shear. Spin contributions explicitly influence the matter distribution; in the spinless limit, the solutions reduce to those of Narlikar and Kuchowicz. For specific parameter values $$n$$ ( $$\sqrt{2}\leq n\leq 2$$ ), the models may be applicable to neutrino geodesic motion and other compact object studies in EC gravity.