Complexity for Dynamical Anisotropic Sphere in f(G,T) Gravity

TL;DR

This paper formulates a complexity factor for dynamical anisotropic spheres within $f(G,T)$ gravity, analyzing how modified gravity terms influence the system's structure, evolution, and stability.

Contribution

It introduces a new complexity measure for anisotropic spheres in $f(G,T)$ gravity, incorporating effects of inhomogeneity, anisotropy, and dark source terms.

Findings

Dark source terms increase system complexity

Complexity free condition can be stable during evolution

Homologous evolution simplifies the system analysis

Abstract

This paper is devoted to the formulation of a complexity factor for dynamical anisotropic sphere in the framework of $f(G,T)$ gravity, where $G$ is the Gauss-Bonnet invariant and $T$ is the trace of energy-momentum tensor. Inhomogeneous energy density, anisotropic pressure, heat dissipation and modified terms create complexity within the self-gravitating system. We evaluate the structure scalars by orthogonal splitting of the Riemann tensor to evaluate a complexity factor which incorporates all the fundamental properties of the system. Moreover, we examine the dynamics of the sphere by assuming homologous mode as the simplest pattern of evolution. We also discuss dissipative as well as non-dissipative scenarios corresponding to homologous and complexity free conditions. Finally, we establish a criterion under which the complexity free condition remains stable throughout the process of evolution. We conclude that the presence of dark source terms of $f(G,T)$ gravity increase the system's complexity.