Stability Analysis of Polytropic Stellar Models in Einstein Gravity Theory

This study presents a class of new feasible solutions to Einstein field equations by incorporating anisotropic fluid distribution within the framework of the general theory of relativity. To achieve this, we utilize a generalized polytropic equation of state along with a particular transformation to make the field equations simpler. We also use a specific spacetime ansatz to close the system as the number of unknowns are still larger than that of equations. We develop several polytropic models by selecting different values for the corresponding index, specifically η = 1, 1/2, 2/3. The junction conditions are also used through which we match the interior and exterior solutions at the hypersurface. Afterwards, we examine various physical properties of the proposed models through graphical analysis, and conclude that they satisfy all the necessary criteria for astrophysical survival.