Construction and physical analysis of complexity control decoupled stellar configurations beyond general relativity

The principal aim of this manuscript is to explore the mechanism of isotropization and the evolution of structural complexity in self-gravitating systems within the framework of 𝑓 ⁡ ( 𝒬 , ℒ 𝑚 ) gravity using the gravitational decoupling technique. To achieve this, an initially anisotropic configuration is modified by introducing an additional source coupled to the seed matter sector through a dimensionless parameter. Two distinct stellar configurations are developed using different metric ansatze: the first is obtained analytically under an isotropization condition, whereas the second is solved numerically under a complexity-preserving constraint. The complexity of the resulting configurations is investigated using Herrera’s structure-scalar framework. Within this approach, the overall complexity is decomposed into two distinct components associated with the seed matter distribution and the decoupling sector. A suitable condition is subsequently imposed on the additional source to ensure that it does not modify the inherent complexity of the seed configuration. The physical viability of the developed models is then evaluated in terms of their regularity, stability, and consistency with observational data for known compact stellar objects.

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