A further study on Palatini f(ℛ)-theories for polytropic stars

Abstract

After briefly reviewing the results about polytropic stars in Palatini f(ℛ)-theories, we first show how these results rely on the assumption of a regular function f(ℛ). In particular, singular models allow to extend the parameter interval in which no singularity is formed.Furthermore, we show how the conformal metric can be matched smoothly in the cases where the original metric generates a singularity. In fact, the singularity comes from a singular conformal factor which is continuous though not differentiable at the stellar surface. This suggests that the correct metric to be considered as physical is the conformal metric.This is relevant because, even when matching the original metric is possible, the use of the conformal metric generates different stellar models.