Dirac stars in modified $F(R)$ gravity
We study Dirac mini-stars in modified $R^2$ gravity, where gravity is sourced by both linear and nonlinear spinor fields. Two-dimensional (2D) and three-dimensional (3D) profiles of the mini-star mass are constructed as functions of the spinor frequency (for the 2D profiles) and the central value of the spinor field (for the 3D profiles) in general relativity and modified gravity for various values of the spinor nonlinearity parameter. We show that the modification of gravity alters the properties of these configurations, while increasing the nonlinearity parameter within the framework of $R^2$ gravity significantly changes the profiles of the spinor and metric functions, the effective energy density, and the dependence of the total mass on the oscillation frequency. The most pronounced changes occur at large values of the nonlinearity parameter.