Unveiling the physical aspects of isotropic polytropes in f(R,G) gravity

This paper explores isotropic polytropes within the framework of the f(R,G) modified gravity theory. We derive the field equations that govern these systems and develop the Lane-Emden equations for both mass (baryonic) density and total energy density, utilizing two different polytropic equations of state. Our analysis shows that the constructed models feature positive and finite density and pressure, which decrease as expected towards the outer boundary, aligning with the typical behavior of self-gravitating objects. Additionally, the energy-momentum tensor meets the required energy conditions, confirming the physical viability of the models. The compactness factor remains below the critical limit, signifying stability and providing insights into gravitational redshift. Analysis of the sound speed confirms adherence to causality, while the adiabatic index indicates a degree of stiffness within the system. These findings advance our understanding of self-gravitating objects in f(R,G) gravity and lay the groundwork for future research in this field.