Implications of modified Gauss–Bonnet gravity on gravastar-like structures: High-energy stability and electromagnetic effects

In this study, we explore the formation and stability of electrically charged, singularity-free, cylindrically symmetric gravastar-like structures as viable alternatives to black holes in the framework of $f(G,T)$ gravity. Here, $G$ represents the Gauss–Bonnet term, while $T$ denotes the trace of the energy–momentum tensor. We construct solutions across three distinct regions, employing an appropriate equation of state (EoS) for each to describe their physical properties. By deriving the metric coefficients and analyzing the equations of motion with the non-conservation law in a cylindrically symmetric spacetime, we examine the impact of electromagnetic fields on entropy, energy, and structural length. Our analysis is relevant to the study of high-energy astrophysical environments, such as relativistic plasma structures, non-local thermodynamic equilibrium (LTE) kinetic conditions, and the interiors of ultra-dense objects. Through a graphical investigation, we demonstrate that cylindrical gravastar-like objects can exist in nature under specific parametric choices within Gauss–Bonnet corrected gravity, contributing to the broader understanding of matter and radiation interactions under extreme conditions. Furthermore, we assess the role of charge in modifying the stability conditions of these compact objects. Through the second derivative of the potential function and the derived constraint equation, we establish that charged gravastar models exhibit enhanced stability compared to their uncharged counterparts, provided appropriate parametric conditions are met. Our findings offer insights into the interplay between modified gravity, such as $f(G,T)$ gravity, and the behavior of energy density profiles influenced by electromagnetic effects in compact charged structures.