A completely deformed anisotropic class one solution for charged compact star: a gravitational decoupling approach

Abstract In this article, we have investigated a new completely deformed embedding class one solution for the compact star in the framework of charged anisotropic matter distribution. For determining of this new solution, we deformed both gravitational potentials as $$\nu ~\mapsto ~\xi +\alpha \, h(r)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ν</mml:mi><mml:mspace/><mml:mo>↦</mml:mo><mml:mspace/><mml:mi>ξ</mml:mi><mml:mo>+</mml:mo><mml:mi>α</mml:mi><mml:mspace/><mml:mi>h</mml:mi><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> and $$e^{-\lambda } \mapsto ~e^{-{\mu }} + \alpha \,f(r)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi>λ</mml:mi></mml:mrow></mml:msup><mml:mo>↦</mml:mo><mml:mspace/><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mi>μ</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>α</mml:mi><mml:mspace/><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> by using Ovalle (Phys Lett B 788:213, 2019) approach. The gravitational deformation divides the original coupled system into two individual systems which are called the Einstein’s system and Maxwell-system (known as quasi-Einstein system), respectively. The Einstein’s system is solved by using embedding class one condition in the context of anisotropic matter distribution while the solution of Maxwell-system is determined by solving of corresponding conservation equation via assuming a well-defined ansatz for deformation function h ( r ). In this way, we obtain the expression for the electric field and another deformation function f ( r ). Moreover, we also discussed the physical validity of the solution for the coupled system by performing several physical tests. This investigation shows that the gravitational decoupling approach is a powerful methodology to generate a well-behaved solution for the compact object.

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