Acceptability Conditions and Relativistic Anisotropic Generalized Polytropes

This paper explored the physical acceptability conditions for anisotropic matter configurations in General Relativity. The study considered a generalized polytropic equation of state $P=\kappa {\rho}^{\gamma}+\alpha \rho -\beta$ for a heuristic anisotropy. We integrated the corresponding Lane-Emden equation and found the parameter-space portion ensuring the configurations' acceptability. Polytropic matter configurations are more stable for total energy density, and small local anisotropies produce acceptable models. Finally, convective disturbances do not generate cracking instabilities.