A model of compact and ultracompact objects in $$f(\mathcal {R})$$ f ( R ) -Palatini theory

We present the features of a model which generalizes Schwarzschild’s homogeneous star by adding a transition zone for the density near the surface. By numerically integrating the modified TOV equations for the $$f(\mathcal {R})=\mathcal {R}+\lambda \mathcal {R}^2$$ Palatini theory, it is shown that the ensuing configurations are everywhere finite. Depending on the values of the relevant parameters, objects more, less or as compact as those obtained in GR with the same density profile have been shown to exist. In particular, in some region of the parameter space the compactness is close to that set by the Buchdahl limit.