Curvature singularities, tidal forces and the viability of Palatini f(R) gravity

In a previous paper we showed that static spherically symmetric objects which, in the vicinity of their surface, are well described by a polytropic equation of state with 3/2 < < 2 exhibit a curvature singularity in Palatini f(R) gravity. We argued that this casts serious doubt on the validity of Palatini f(R) gravity as a viable alternative to general relativity. In the present paper, we further investigate this characteristic of Palatini f(R) gravity in order to clarify its physical interpretation and consequences.