Stability of Anisotropy Pressure in Self-Gravitational Systems in f(G) Gravity

This investigation aims to explore certain variables which are considered responsible for generating pressure anisotropy in dynamical spherically symmetric stellar systems against the background of the stringy-inspired Gauss–Bonnet modification of general relativity. We explore the hydrostatic equilibrium of self-gravitating systems by taking into account the modified form of Tolman–Oppenheimer–Volkoff for the quadratic-f(G) gravitational model. In this respect, we formulate a differential equation in terms of the Weyl curvature scalar, also described as an evolution equation, which is essential for understanding the evolution of the stellar structure. Finally, we conclude that the existence of some fluid variables such as shear, heat flux and the irregular behavior of energy density in the presence of an extra degree f(G)-terms in the fluid flow that are the elements that cause anisotropy in the initially isotropic stellar structure. The comparison of the presented results with those of the classical model shows that they are physically relevant and compatible.