Stellar structure model in hydrostatic equilibrium in the context of $f(\mathcal{R})$-gravity
In this work we present a stellar structure model from $f(\mathcal{R})$-gravity point of view capable to describe some classes of stars (White Dwarfs, Brown Dwarfs, Neutron stars, Red Giants and the Sun). This model was based on $f(\mathcal{R})$-gravity field equations for $f(\mathcal{R})= \mathcal{R}+ f_2 \mathcal{R}^2$, hydrostatic equilibrium equation and a polytropic equation of state. We compared the results obtained with those found by the Newtonian theory. It has been observed that in these systems, where high curvature regimes emerge, stellar structure equations undergo modifications. Despite the simplicity of this model, the results were satisfactory. The estimated values of pressure, density and temperature of the stars are within those determined by observations. This $f(\mathcal{R})$-gravity model has been proved to be necessary to describe stars with strong fields such as White Dwarfs, Neutron stars and Brown Dwarfs, while stars with weaker fields, such as Red Giants and the Sun, were best described by the Newtonian theory.