Physical attributes of polytropic structures in $$\mathbb {F}(R)$$ theory of gravity

Abstract The aim of this work is to study the general formalism and applications of polytropic stars within the framework of a well-famed modified theory of gravity namely $$\mathbb {F}(R)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> theory. To accomplish this task, we assume the static spherically symmetric and Schwarzschild spacetimes, respectively, for defining the star’s interior and exterior geometries. By applying two polytropic equations of state, we derive physically well-behaved solutions to $$\mathbb {F}(R)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> field equations. Firstly, we develop the hydrostatic equilibrium and Lane–Emden equations for the isotropic fluid case within this framework of gravity. Next, we analyze the impact of isotropic pressure on stellar structures and graphically assess the physical behavior of isotropic polytropes using energy conditions and stability criteria. Additionally, the physical acceptability conditions are examined for the proposed solutions. The results indicate that this theory produces more viable and stable polytropes as compared to general relativity.