Hydrostatic equilibrium and stellar structure in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>gravity

We investigate the hydrostatic equilibrium of stellar structure by taking into account the modified Lan\'e-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 $f(R)\ensuremath{\rightarrow}R$, becomes the standard Lan\'e-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.

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