Cracking of charged polytropes with generalized polytropic equation of state

We discuss the occurrence of cracking in charged anisotropic polytropes with generalized polytropic equation of state through two different assumptions; (i) by carrying out local density perturbations under a conformally flat condition (ii) by perturbing anisotropy, polytropic index and charge parameters. For this purpose, we consider two different definitions of polytropes that exist in literature. We conclude that under local density perturbations scheme cracking does not appear in both types of polytropes and stable configuration is observed, while with the second type of perturbation cracking appears in both types of polytropes under certain conditions. (orig.)