A no-go theorem for polytropic spheres in Palatini f(R) gravity

TL;DR

This paper demonstrates that in Palatini f(R) gravity, most common equations of state do not admit physically acceptable static spherically symmetric solutions, challenging its viability as an alternative to General Relativity.

Contribution

It establishes a no-go theorem showing the non-existence of solutions for generic f(R) functions in Palatini gravity for typical equations of state.

Findings

Most equations of state lack solutions in Palatini f(R) gravity

Solutions only exist in the special case of General Relativity

Questions the viability of Palatini f(R) as an alternative gravity theory

Abstract

Non-vacuum static spherically-symmetric solutions in Palatini f(R) gravity are examined. It is shown that for generic choices of f(R), there are commonly-used equations of state for which no satisfactory physical solution of the field equations can be found within this framework, apart from in the special case of General Relativity, casting doubt on whether Palatini f(R) gravity can be considered as giving viable alternatives to General Relativity.