Hydrostatic equilibrium and stellar structure in f(R) gravity

We investigate the hydrostatic equilibrium of stellar structure by taking into account the modified Lane-Emden equation coming out from f(R) gravity. Such an equation is obtained in a metric approach by considering the Newtonian limit of f(R) gravity, which gives rise to a modified Poisson equation, and then introducing a relation between pressure and density with polytropic index n. The modified equation results an integro-differential equation, which, in the limit f(R) -> R, becomes the standard Lane-Emden equation. We find the radial profiles of the gravitational potential by solving for some values of n. The comparison of solutions with those coming from general relativity shows that they are compatible and physically relevant.