Role of vanishing complexity factor in generating spherically symmetric gravitationally decoupled solution for self-gravitating compact object

Abstract In this work, we study the role of the vanishing complexity factor in generating self-gravitating compact objects under gravitational decoupling technique in f ( Q )-gravity theory. To tackle the problem, the gravitationally decoupled action for modified f ( Q ) gravity has been adopted in the form $${\mathscr {S}}={{\mathscr {S}}_{Q}}+{{\mathscr {S}}^{*}_{\theta }}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>Q</mml:mi> </mml:msub> <mml:mo>+</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mi>θ</mml:mi> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> , where $${\mathscr {S}}_Q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>Q</mml:mi> </mml:msub> </mml:math> denotes the Lagrangian density of the fields which appears in the f ( Q ) theory while $${\mathscr {S}}^{*}_{\theta } (=\alpha {\mathscr {S}}_{\theta }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mi>θ</mml:mi> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>=</mml:mo> <mml:mi>α</mml:mi> </mml:mrow> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>θ</mml:mi> </mml:msub> </mml:mrow> </mml:math> , where $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> is just a coupling parameter which controls the deformation) describes the Lagrangian density for a new kind of gravitational sector which has not been included in f ( Q ) gravity. After that, we developed an important relation between gravitational potentials via a systematic approach (Contreras and Stuchlik in Eur Phys J C 82:706, 2022) using the vanishing complexity factor condition in the context of f ( Q ) theory. We have used the Buchdahl model along with the mimic-to-density constraints approach for generating the complexity-free anisotropic solution. The qualitative physical analysis has been done along with the mass-radius relation for different compact objects via $$M-R$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>-</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> curves to validate our solution. It is noticed that the coupling constant $$\beta _1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>β</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> has a definite impact on constraining the mass and radii of the object that are shown in $$M-R$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>-</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> curves. The obtained results show that the compactness of the objects can be controlled by the coupling parameters.

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