Electromagnetic field on the complexity of minimally deformed compact stars

Abstract In the context of this endeavor, we establish a simple protocol for formulating interior stellar solutions that exhibit spherically symmetric configurations against the backdrop of relativistic gravitational decoupling through radial metric deformation (minimal geometric deformation scheme). In this pursuit, we make use of the vanishing complexity factor ( $$\widetilde{Y}_{TF}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>Y</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mrow> <mml:mi>TF</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) condition, based on Herrera’s (Phys Rev D 97, 044010, 2018) innovative concept regarding the complexity of static or slowly evolving spherical matter configurations. The idea of a complexity factor emerges as the outcome of the orthogonal splitting of the Riemann–Christoffel tensor, which yields different scalar functions, known as structure scalars. The protocol is demonstrated by employing the Buchdahl and Tolman relativistic stellar ansatzes as isotropic seeds. Both of these ansatzes exhibit similar physical features, with a minor variation in their magnitudes in the case of $$\widetilde{Y}_{TF}\ne 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mover> <mml:mi>Y</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mrow> <mml:mi>TF</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≠</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , where $$0\le \alpha &lt;1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>α</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , and $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> represents a coupling parameter. However, when $$\widetilde{Y}_{TF}=0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mover> <mml:mi>Y</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mrow> <mml:mi>TF</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , the Buchdahl stellar ansatz exhibits a uniform density matter configuration, while the Tolman model features an increasing pressure profile. The obtained relativistic stellar models satisfy the basic viability constraints required for the physically realistic configurations.

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