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

M. M. M. Nasir; M. Zeeshan Gul; Orhan Donmez; Faisal Javed; Bander Almutairi

doi:10.1140/epjc/s10052-025-13899-3

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 189
https://doi.org/10.1140/epjc/s10052-025-13899-3

Regular Article - Theoretical Physics

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

M. M. M. Nasir¹, M. Zeeshan Gul²^,6^a, Orhan Donmez³, Faisal Javed⁴^b and Bander Almutairi⁵

¹ Department of Mathematics, University of Management and Technology, Johar Town, 54782, Lahore, Pakistan
² Department of Mathematics and Statistics, The University of Lahore, 1-KM Defence Road, 54000, Lahore, Pakistan
³ College of Engineering and Technology, American University of the Middle East, 54200, Egaila, Kuwait
⁴ Department of Physics, Zhejiang Normal University, 321004, Jinhua, People’s Republic of China
⁵ Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia
⁶ Research Center of Astrophysics and Cosmology, Khazar University, 41 Mehseti Street, AZ1096, Baku, Azerbaijan

^a mzeeshangul.math@gmail.com
^b faisaljaved.math@gmail.com

Received: 12 January 2025
Accepted: 2 February 2025
Published online: 15 February 2025

Abstract

In this paper, we evaluate the complexity of the anisotropic static cylindrical geometry in the framework of $f (G)$ $f(\mathcal {G})$ gravity, where $G$ $\mathcal {G}$ 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 $f (G)$ $f(\mathcal {G})$ gravity. Furthermore, we used the Weyl tensor and obtained different structure scalars by orthogonally splitting the Riemann tensor. One of these scalars, $Y_{TF}$ $Y_{TF}$ , 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.

© The Author(s) 2025

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