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

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 or low mass brown dwarf 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.