$F(\Mathcal{G},T_{\Alpha\Beta}T^{\Alpha\Beta})$ Theory and Complex Cosmological Structures

The basic objective of this investigation is to explore the impactof a novel gravitational modification, specifically, the$f(\mathcal{G}, \mathbf{T}^2)$ (where $\mathcal{G}:=\mathbf{R}^{2}+R_{\alpha\beta\sigma\varsigma}R^{\alpha\beta\sigma\varsigma}-4R_{\alpha\beta}R^{\alpha\beta}$and $\mathbf{T}^2 :=T_{\alpha\beta}T^{\alpha\beta}$, $T^{\alpha\beta}$ denotes thestress-energy tensor) model of gravitation, upon the complexity oftime-dependent dissipative as well as non-dissipative sphericallysymmetric celestial structures. To find the complexity factor$(\mathbb{C}_{\mathbf{F}})$ from the generic version of thestructural variables, we performed Herrera's scheme for theorthogonal cracking of Riemann tensor. In this endeavor, we aremainly concerned with the issue of relativistic gravitationalcollapse of the dynamically relativistic spheres fulfilling thepresumption of minimal $\mathbb{C}_{\mathbf{F}}$. The incorporationof a less restrictive condition termed as quasi-homologous$(\mathbb{Q}_{\mathbf{H}})$ condition together with the zero$\mathbb{C}_{\mathbf{F}}$, allows us to formulate a range of exactsolutions for a particular choice of $f(\mathcal{G}, \mathbf{T}^2)$model. We find that some of the given exact solutions relax theDarmois junction conditions and describe thin shells by satisfyingthe Israel conditions, while some exhibit voids by fulfilling theDarmois constraints on both boundary surfaces. Eventually, fewexpected applications of the provided solutions in the era of moderncosmology are debated