  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<Gamma<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.
