Implications of Complexity Factor on Evolution of New Dynamical and Static Wormholes in $f(R, T)$ Gravity

Abstract

This study presents new spherically symmetric and dynamical wormhole solutions supported by ordinary matter modeled as an anisotropic fluid, exhibiting a traversable nature. To achieve this goal, we adopt different approaches to obtain both evolving static and genuinely dynamical solutions, such as imposing a viable condition on the Ricci scalar, considering an anisotropic equation of state, and choosing a suitable energy density profile. For each derived shape function, we analyze the corresponding $2D$ and $3D$ embedding diagrams and verify their compatibility with the weak energy condition through density plots. The equilibrium conditions are also explored graphically to assess the stability of the obtained solutions, which are shown to be stable within the analyzed framework. Additionally, we investigate the complexity factor associated with each configuration, examining its dependence on both temporal evolution and the coupling parameter $\lambda$ of the $f(R,T)$ theory.