Extended gravitational decoupling (GD) solution for charged compact star model

In the present article, we have obtained a new solution for the charged compact star model through the gravitational decoupling (GD) by using a complete geometric deformation (CGD) approach (Ovalle, Phys Lett B 788:213, 2019). In this approach, the initial decoupled system is separated into two subsystems namely Einstein–Maxwell’s system and quasi-Einstein system. We solve Einstein–Maxwell’s system by taking well known Tolman–Kuchowicz spacetime geometry in the context of the perfect fluid matter distribution. On the other hand, the second system introduce the anisotropy inside the matter distribution which is solved by taking an EOS in θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta $$\end{document} components. The boundary conditions have been derived to determine the constants parameter. To support the mathematical and physical analysis of the present GD solution, we have plotted all the graphs for the compact objects PSR J1614-2230, 4U1608-52 and Cen X-3 corresponding to the constant α=0.001\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =0.001$$\end{document}, 0.0012 and 0.0014, respectively. Moreover, we also studied the equilibrium and stability of the solution. The present study shows that the GD technique is a very significant tool to generalize the solution in a more complex form or one matter distribution to another matter distribution.