Stability of relativistic spheres powered by energy profile in Einstein Gauss–Bonnet gravity

In this paper, we study the dynamical irregularity of the locally anisotropic spherical fluids in the context of Einstein–Gauss–Bonnet theory. We aim to describe the causes of energy-density irregularity of self-gravitating fluids and explain how those causes evolved from a homogeneous distribution at first. After computing field equations, we formulate two independent components of evolution equations. This expression involves the Weyl tensor and dynamical variables that would lead us to explain the emergence of inhomogeneity patterns. The relevant quantities involved in the irregularities within the initially homogeneous system are analyzed by considering particular nondissipative and dissipative distribution cases. We find the theoretical irregularity factor consistent with astrophysical observations. With this relation, it is explicitly demonstrated that in the presence of Einstein–Gauss–Bonnet gravity terms, the inhomogeneity term decreases its role gradually as the observer moves away from the center towards the boundary surface.