Analyzing the impact of Gauss–Bonnet corrections on structure scalars admitting the zero complexity condition

Abstract In this paper, we evaluate the complexity of the anisotropic static cylindrical geometry in the framework of $$f(\mathcal {G})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity, where $$\mathcal {G}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>G</mml:mi> </mml:math> represents the Gauss–Bonnet term. In this perspective, we calculate modified field equations, the C energy formula, the Tolman–Oppenheimer–Volkoff equation, and the mass function that help to understand the astrophysical structures in $$f(\mathcal {G})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity. Furthermore, we used the Weyl tensor and obtained different structure scalars by orthogonally splitting the Riemann tensor. One of these scalars, $$Y_{TF}$$ <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 referred to as the complexity factor. This parameter measures system complexity due to non-uniform energy density and non-isotropic pressure. Using the constraint of the variable of vanishing complexity, time-independent solutions are derived for the Gokhroo–Mehra model. It is found that the presence of corrective terms reduce the complexity of the system.

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