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

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.

28 pages

References in corpus (30)

• Modified Gauss-Bonnet theory as gravitational alternative for dark energy
• A Statistical Measure of Complexity
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• Can modified gravity explain accelerated cosmic expansion?
• Reconciling dark energy models with f(R) theories
• Spherically symmetric dissipative anisotropic fluids: A general study
• New definition of complexity for self-gravitating fluid distributions: The spherically symmetric, static case
• Structure and evolution of self-gravitating objects and the orthogonal splitting of the Riemann tensor
• Features of the Extension of a Statistical Measure of Complexity to Continuous Systems
• Definition of complexity for dynamical spherically symmetric dissipative self-gravitating fluid distributions
• Tendency to Maximum Complexity in a Non-Equilibrium Isolated System
• Brane versus shell cosmologies in Einstein and Einstein-Gauss-Bonnet theories
• Ghosts, Instabilities, and Superluminal Propagation in Modified Gravity Models
• On the stability of the shear-free condition
• Conformally flat polytropes for anisotropic matter
• Statistical complexity, Fisher-Shannon information, and Bohr orbits in the H-atom
• Cylindrically Symmetric Relativistic Fluids: A Study Based on Structure Scalars
• Complexity factors for axially symmetric static sources
• Solar System Constraints on Gauss-Bonnet Mediated Dark Energy
• Exploring Cylindrical Solutions in Modified f(G) Gravity
• Viable and Stable Compact Stars in $f(\mathcal{Q})$ Theory
• A simple protocol to construct solutions with vanishing complexity by Gravitational Decoupling
• Uncharged and charged anisotropic like--Durgapal stellar model with vanishing complexity
• Complexity Factor For Anisotropic Source in Non-minimal Coupling Metric $f(R)$ Gravity
• Viable and Stable Compact Stellar Structures in $f(\mathcal{Q},\mathcal{T})$ Theory
• Bondi-Hoyle Accretion around the Non-rotating Black Hole in 4D Einstein-Gauss-Bonnet Gravity
• Observational analysis of late-time acceleration in $f(Q,L_m)$ gravity
• Complexity of Dynamical Dissipative Cylindrical System in Non-minimally Coupled Theory
• Observational constraints on the equation of state of viscous fluid in $f(R,T)$ gravity
• Mixed potentials in radiative stellar collapse