Dirac star in $R^2$ gravity

Stationary compact strongly gravitating configurations supported by two spinor fields are studied. The latter are described by a special ansatz permitting the obtaining of spherically symmetric solutions with a diagonal energy-momentum tensor. The consideration is carried out within the framework of the theories of Einstein’s gravity and modified $R^2$ gravity. In both theories, we obtain regular asymptotically flat solutions describing objects with finite masses and sizes. The dependencies of the mass of the configurations under investigation on the oscillation energy of the spinor fields are constructed. The distributions of the metric functions and the spinor fields along the radius of the systems are calculated. The distinctions in physical characteristics of the obtained configurations appearing due to the modification of the gravity are revealed.