Influence of f(G) gravity on the complexity of relativistic self-gravitating fluids

Abstract

In this paper, we extend the notion of complexity for the case of nonstatic self-gravitating spherically symmetric structures within the background of modified Gauss–Bonnet gravity (i.e. [Formula: see text] gravity), where [Formula: see text] denotes the Gauss–Bonnet scalar term. In this regard, we have formulated the equations of gravity as well as the relations for the mass function for anisotropic matter configuration. The Riemann curvature tensor is broken down orthogonally through Bel’s procedure to compose some modified scalar functions and formulate the complexity factor with the help of one of the scalar functions. The CF (i.e. complexity factor) comprehends specific physical variables of the fluid configuration including energy density inhomogeneity and anisotropic pressure along with [Formula: see text] degrees of freedom. Moreover, the impact of the dark source terms of [Formula: see text] gravity on the system is analyzed which revealed that the complexity of the fluid configuration is increased due to the modified terms.

Analysis of hyperbolically symmetric fluid configurations in modified Gauss–Bonnet gravity

“…Equation (16) shows that the mass function m(r ) is a positive quantity, then it follows that the quantity ρ should be negative and consequently the weak energy condition is violated, as already discussed in [59]. In this respect, several comments are discussed in [44] that allows us to right the mass function in the following form m(r…”

“…In addition, this form is also be used for understanding the unification of primordial inflation and late-time DE era [54]. Such types of GBG corrections may be used as possible toy models for studying the formation of complex cosmic structures well as the dark section (the puzzles of DM and DE) of our universe [16,55,56]. Just like Einstein's GR, the modified GBG cosmological model is also conserved (see [57,58] and references therein), i.e., ∇ μ T eff μη = 0 that provides a generalized hydrostatic continuity equation corresponding to the considered hysterically symmetric static source as…”

“…Some modified GBG models of the late-time cosmological evolution are also predicted by low-energy effective string theory action [14]. The modified versions of GBG cosmologies can be used for understanding the evolution of complex self-gravitational systems with the help of structure scalars as well as gravitational waves' events [15][16][17][18][19][20][21].…”

“…This novel scheme of complexity is based on the fundamental assumption that less complex systems comprises of homogeneous (in the energy density) and isotropic pressure fluid configurations. The perspective applications regarding the complexity of self-gravitational systems within the frameworks of different geometrically modified gravitational models has been discussed in detail [16][17][18][19][20][21]. This investigation is endeavored to analyze the physical features of locally anisotropic, hyperbolically symmetric self-gravitational fluids in terms of geometrical and physical variables that seem to play a significant role in the evolution of such objects.…”

Stability Analysis of Isotropic Spheres in Einstein Gauss–Bonnet Gravity

“…Nashed and Capozziello [ 46 ] constructed anisotropic compact relativistic structure solutions in $$f(\mathbf {R})$$‐gravity under spherically symmetric background using hydrostatic equilibrium equation. Bhatti and his collaborators [ 47 ] discussed the evolution of anisotropic complex self‐gravitational systems by measuring a scalar function emerging from the orthogonal partitioning of curvature tensor for cosmological $$f(\mathcal {G})$$‐theory. They also explored the dynamics of complex self‐gravitating cosmological systems by identifying the complexity factor within the dynamics of $$f(\mathcal {G},T)$$ theory of gravitation.…”