Isotropization and complexity shift of gravitationally decoupled charged anisotropic sources

Abstract This article focuses on investigating the role of decoupling in isotropizing anisotropic, self-gravitational charged sources with spherical symmetry through a well-known gravitational technique, known as minimal geometric deformation (MGD). This technique separates the given system into two gravitational systems: the Einstein-Maxwell system and the gravitational system governed by additional source. We employ novel approaches, including the zero complexity factor and isotropization techniques, to construct various charged compact star models using the Tolman IV as the seed source within the framework of the MGD scheme. The term complexity factor emerges as one of the structure-defining scalar quantities resulting from the orthogonal splitting of the Riemann–Christoffel curvature tensor, as proposed by Herrera (Phys Rev D 97(4):044010, 2018). This scalar function, denoted as $$Y_{TF}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Y</mml:mi> <mml:mrow> <mml:mi>TF</mml:mi> </mml:mrow> </mml:msub> </mml:math> , is associated with the fundamental structural characteristics of self-gravitational compact configurations. Our approach is innovative in that it derives the deformation functions by imposing the requirement of $$Y_{TF}=0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Y</mml:mi> <mml:mrow> <mml:mi>TF</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> and employs isotropization techniques for electrically charged anisotropic configurations.

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