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.

In this paper, we study the cracking of compact object PSR J1614-2230 in quadratic regime with electromagnetic field. For this purpose, we develop a general formalism to determine the cracking of charged compact objects. We apply local density perturbations to hydrostatic equilibrium equation as well as physical variables involve in the model. We plot the force distribution function against radius of the star with different parametric values of model both with and without charge. It is found that PSR J1614-2230 remains stable (no cracking) corresponding to different values of parameters when charge is zero, while it exhibit cracking (unstable) when charge is introduced. We conclude that stability region increases as amount of charge increases.

A framework is developed for generalized polytropes with the help of complexity factor introduced by Herrera (Phy Rev D 97:044010, 2018), by using the spherical symmetry with anisotropic inner fluid distribution. For this purpose generalized polytropic equation of state will be used, having two cases (i) for mass density (μ o ), (ii) for energy density (μ), each case leads to a system of differential equations. These systems of differential equations involve two equations with three unknowns and they will be made consistent by using the complexity factor. The analysis of the solutions of these systems will be carried out graphically by using different parametric values involved in the systems.

We examine the impact of electromagnetic field on the stability of compact stars corresponding to embedded class one metric using the concept of cracking. For this purpose, we develop the generalized hydrostatic equilibrium equation for charged perfect fluid distribution of compact stars and perturb it by means of local density perturbation scheme to check the stability of inner matter configuration. We investigate the cracking of Her X-1,