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 for several hundred models and found the parameter-space portion ensuring the configurations' acceptability. Polytrope based on the total energy density are more stable than those with baryonic density, and small positive local anisotropies produce acceptable models. We also found that polytropic configurations where tangential pressures are greater than radial ones are also more acceptable. Finally, convective disturbances do not generate cracking instabilities. Several models emerging from our simulations could represent candidate of astrophysical compact objects.