Study of Complexity Factor and Stability of Dynamical Systems in $f(G)$ Gravity

TL;DR

This paper investigates the complexity and stability of non-static cylindrical systems in $f(G)$ gravity, introducing a complexity factor based on structure scalars and analyzing conditions for homogeneous and isotropic evolution.

Contribution

It defines a new complexity scalar in $f(G)$ gravity and explores conditions for stable, homogeneous evolution of anisotropic, dissipative systems.

Findings

Complexity factor $YTF$ measures system complexity due to anisotropy and density inhomogeneity.

Homologous evolution corresponds to isotropic, shear-free, and homogeneous configurations.

Dissipative systems can remain geodesic with shear, leading to diverse solutions.

Abstract

In this paper, we evaluate the complexity of the non-static cylindrical geometry with anisotropic matter configuration in the framework of modified Gauss-Bonnet theory. In this perspective, we calculate modified field equations, the C energy formula, and the mass function that helps to understand the astrophysical structures in this modified gravity. Furthermore, we use the Weyl tensor and obtain different structure scalars by orthogonally splitting the Riemann tensor. One of these scalars, $YTF$ is referred to as the complexity factor. This parameter measures the system's complexity due to non-uniform energy density and non-isotropic pressure. We select the identical complexity factor for the structure as used in the non-static scenario while considering the analogous criterion for the most elementary pattern of development. This technique involves formulating structural scalars that illustrate the fundamental features of the system. A fluid distribution that satisfies the vanishing complexity requirement and evolves homologously is characterized as isotropic, geodesic, homogeneous, and shear-free. In the dissipative scenario, the fluid remains geodesic while exhibiting shear, resulting in an extensive array of solutions.