Probing Electrically Charged Gravastars and Their Physical Features in <i>f</i> ( <i>G</i> ) Theory

In this manuscript, we investigate cylindrically symmetric, electrically charged gravitational vacuum compact objects proposed as viable alternatives to black holes under the influence of f(G) gravity, where G denotes the Gauss-Bonnet (GB) invariant. We consider specific models consisting of three distinct regions, each characterized by an appropriate equation of state, to describe the compact configuration. The metric coefficients for each region are explicitly derived, along with the corresponding equations of motion and conservation relations for a perfect matter distribution. We also examine the effects of the electromagnetic field on thermodynamic quantities such as entropy, energy, and characteristic length scales through graphical analysis, indicating that such cylindrical structures may exist with suitable parametric choices. The influence of electric charge on the stability domain of these relativistic structures is explored by analyzing the second derivative of the potential function and an associated constraint equation. The results demonstrate that charged compact models can achieve enhanced stability compared to their uncharged counterparts for suitable parameter selections.