This study investigates the stability of thin-shell wormholes within anti-de Sitter spacetime, utilizing the Hayward Letelier black hole framework. Our findings reveal that the stability of thin-shell wormholes is notably influenced by the choice of equation of state governing the matter distribution. We confirm the satisfaction of basic constraints for traversable wormholes, with significant violations of the null and weak energy conditions, indicating the presence of exotic matter. Through a detailed analysis of various equations of state, including barotropic, phantom-like, and variable Chaplygin formulations, we elucidate how parameters such as the Hayward parameter, cloud of string parameter, and the AdS length scale parameter affect the dynamic behavior and stability of these structures. The results show that barotropic distributions maintain stability up until the formation of an event horizon, while phantom-like equation of state exhibits complex stability trends based on parameter values. Notably, the variable Chaplygin equation of state demonstrates more stable configurations at higher values of its variable constant compared to other models. These insights contribute to a deeper understanding of the conditions necessary for the existence and stability of thin-shell wormholes, providing a foundation for future research into exotic structures in gravitational physics and cosmology.
Houedokou et al. (Sat,) studied this question.
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