The aim of this paper is to generalize the definition of complexity for the static self-gravitating structure in f(R, T, Q) gravitational theory, where R is the Ricci scalar, T is the trace part of energy momentum tensor and Q ≡ R_αβT^αβ. In this context, we have considered locally anisotropic spherical matter distribution and calculated field equations and conservation laws. After the orthogonal splitting of the Riemann curvature tensor, we found the corresponding complexity factor with the help of structure scalars. It is seen that the system may have zero complexity factor if the effects of energy density inhomogeneity and pressure anisotropy cancel the effects of each other. All of our results reduce to general relativity on assuming f(R, T, Q) = R condition.

In this paper, we explore the existence of various non-singular compact stellar solutions influenced by the Maxwell field within the matter-geometry coupling based modified gravity. We start this analysis by considering a static spherically symmetric spacetime which is associated with the isotropic matter distribution. We then determine the field equations corresponding to two specific functions of this modified theory. Along with these models, we also adopt different forms of the matter Lagrangian. We observe several unknowns in these equations such as the metric potentials, charge and fluid parameters. Thus, the embedding class-one condition and a particular realistic equation of state is used to construct their corresponding solutions. The former condition provides the metric components possessing three constants, and we calculate them through junction conditions. Further, four developed models are graphically analyzed under different parametric values. Finally, we find all our developed solutions well-agreeing with the physical requirements, offering valuable insights for future explorations of the stellar compositions in this theory.

This paper formulates three different analytical solutions to the gravitational field equations in the framework of Rastall theory by taking into account the gravitational decoupling approach. For this, the anisotropic spherical interior fluid distribution is assumed as a seed source characterized by the corresponding Lagrangian. The field equations are then modified by introducing an additional source which is gravitationally coupled with the former fluid setup. Since this approach makes the Rastall equations more complex, the MGD scheme is used to tackle this, dividing these equations into two systems. Some particular ansatz are taken into account to solve the first system, describing initial anisotropic fluid. These metric potentials contain multiple constants which are determined with the help of boundary conditions. On the other hand, the solution for the second set is calculated through different well-known constraints. Afterwards, the estimated data of a pulsar 4U 1820-30 is considered so that the feasibility of the developed models can be checked graphically. It is concluded that all resulting models show physically acceptable behavior under certain choices of Rastall and decoupling parameters.

This paper introduces the concept of complexity for a static spherical spacetime and extends it to the modified $$f({\textbf{R}})$$f ( R ) framework. The formulation of the corresponding field equations is then carried out to describe the anisotropic interior. The spherical mass function is defined in both geometric as well as matter terms. Utilizing the orthogonal splitting of the curvature tensor, specific scalars are developed, with one of them denoted as $${\mathcal {Y}}_{TF},$$Y TF , identified as the complexity factor for the considered fluid setup. In addressing the system of field equations admitting some extra degrees of freedom, the complexity-free condition is introduced. In conjunction with this condition, three other constraints are applied, leading to the development of different models. We also provide a graphical representation of the resulting solutions, using specific parametric values. From this analysis, we conclude that our all three models exhibit the properties required for the existence of physically viable and stable structures for certain values of the model parameter.