Role of strong matter-field coupling on axial complex systems

Even though extended gravity theories have come up with different healthy measures of complexity for spherical and non-spherical systems, the study of complexity factors for axially symmetric bodies under the influence of strong matter-field coupling is still up for debate. The formation of complexity factors for static axially symmetric bodies is induced by the cracking of the Riemann curvature tensor in an orthogonal manner as initiated by Herrera et al. [Phys. Rev. D 99, 044049(2019)]. We provide the continuation of this work in the f(R, T, Q) gravitational theory, where Q = R${}_{\gamma \varrho }$T${}^{\gamma \varrho }$ that indicates the powerful matter-field coupling due to the bilateral influence of the curvature and matter tensors. We proceed our analysis by considering axial geometry confined with anisotropic fluid constituents. In this context, we compute the field equations for the system under discussion. To examine the source's energy content, two dynamical equations that correspond to independent coordinates are constructed. The curvature tensor is split into tensorial quantities to formulate the scalar functions (structure scalars), which involve the physical attributes of the source in the domain of high curvature regimes. Among all, three of the scalars Y${}_{T{F}_j}$'s (j = 1, 2, 3) are nominated as complexity factors, whose inclusion enhances the inhomogeneity of the propagating system. The vanishing complexity factors criteria are set out for the specific form of the cosmic model that provides the favorable setting to minimize the system's complexity and boost its stability. Furthermore, some analytical insights under various backgrounds of the matter spheroids are presented. (© 2023 Wiley‐VCH GmbH.)