Reexamination of polytropic spheres in Palatini $f(R)$ gravity

We investigate spherically symmetric, static matter configurations with polytropic equation of state for a class of $f(R)$ models in Palatini formalism and show that the surface singularities recently reported in the literature are not physical in the case of Planck scale modified Lagrangians. In such cases, they are just an artifact of the idealized equation of state used. In fact, we show that for the models $f(R)=R\pm \lambda R^2$, with $\lambda$ on the order of the Planck length squared, the presence of a single electron in the Universe would be enough to cure all stellar singularities of this type. From our analysis it also follows that the stellar structure derived from these Lagrangians is virtually undistinguishable from that corresponding to general relativity. For ultraviolet corrected models far from the Planck scale, however, the surface singularities may indeed arise in the region of validity of the polytropic equation of state. This fact can be used to place constraints on the parameters of particular models.