Role of vanishing complexity factor in generating spherically symmetric gravitationally decoupled solution for self-gravitating compact object
S. K. Maurya, Abdelghani Errehymy, Baiju Dayanandan, Saibal Ray, Nuha Al‐Harbi, Abdel‐Haleem Abdel‐Aty
Abstract
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.