The aim of this paper is to discuss the theory of Newtonian and relativistic polytropes with a generalized polytropic equation of state. For this purpose, we formulated the general framework to discuss the physical properties of polytropes with an anisotropic inner fluid distribution under conformally flat condition in the presence of charge. We investigate the stability of these polytropes in the vicinity of a generalized polytropic equation through the Tolman mass. It is concluded that one of the derived models is physically acceptable.

In this paper, we investigate the role of electromagnetic field on the stability regions of charged selfgravitating compact objects by using the concept of cracking. For this purpose, we have applied local density perturbation scheme to the hydrostatic equilibrium equation as well as on physical parameters involved in the model. In particular, we have examined the cracking of charged compact objects like PSR J1614-2230, PSR J1903+327, Vela X-1, SMC X-1 and Cen X-3 with different values of charge. We conclude that these objects exhibit cracking and stability regions decreases with the increase of charge.

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In this paper, we investigate the gravitational behavior of compact objects with the help of generalized polytropic equation of state in isotropic coordinates. We found three exact solutions of Einstein field equations by taking into account the different values of polytropic index with spherically symmetric anisotropic inner fluid distribution. We have regained the masses of PSR J1614 − 2230, Vela X-1, Vela 4U, PSR J1903+327 and 4U 1820-30. Speed of sound has been used to analyze the stability of models. The comprehensive analysis indicates that all the models are physically viable and well behaved.

In this paper, generalized polytropic equation of state is used to get new classes of polytropic models from the solution of Einstein-Maxwell field equations for charged anisotropic fluid configuration. The models are developed for different values of polytropic index n = 1, 1 2 , 2. Masses and radii of eight different stars have been regained with the help of developed models. The speed of sound technique and graphical analysis of model parameters is used for the viability of developed models. The analysis of models indicates they are well behaved and physically viable.