# The Palatini star: exact solutions of the modified Lane-Emden equation

## TL;DR

This paper derives exact solutions for specific cases of the Palatini-modified Lane-Emden equation and compares the properties of Palatini-Newtonian neutron stars with classical Newtonian models, revealing that negative parameters lead to heavier and larger stars.

## Contribution

It provides the first exact solutions for the Palatini-modified Lane-Emden equation for n=0 and n=1, and applies these to model neutron stars within this modified gravity framework.

## Key findings

- Palatini-Newtonian neutron stars are heavier and larger for negative Starobinsky parameters.
- Exact solutions for n=0 and n=1 cases of the modified Lane-Emden equation.
- Comparison shows significant differences from classical Newtonian models.

## Abstract

Two exact solutions for $n=0$ and $n=1$ of the Palatini-modified Lane-Emden equation are found. We have employed these solutions to describe a Palatini-Newtonian neutron star and compared the result with the pure Newtonian counterpart. It turned out that for the negative parameter of the Starobinsky model the star is heavier and larger.