Effects of charge on the complexity of dynamical sphere in energy-momentum squared gravity

In this paper, we investigate how the electromagnetic field influences the idea of complexity within the framework of squared gravity. The physical traits, including heat dissipation, charge, anisotropic pressure, energy density variations and correction components are found to be significant contributors of complexity in celestial objects. By employing Herrera's orthogonal splitting approach, scalar functions are obtained yielding a complexity factor that incorporates the crucial attributes of the self-gravitating system. Furthermore, we examine the dynamics of charged spherical configuration by considering homologous mode as the simplest evolutionary pattern. Our investigation includes complexity-free scenarios (dissipative/non-dissipative) with homologous constraints. Moreover, we explore the components that contribute toward complexity during the evolutionary process. We conclude that self-gravitating structures get more complex with the inclusion of extra curvature terms of squared gravity and charge.