Imprints of deformation parameters on stability and dynamical evaluation of Schwarzschild-AdS thin-shell wormholes

Abstract This study is devoted to developing the geometry of thin-shell wormholes created by combining two deformed Schwarzschild-AdS black holes. We show that the existence of exotic matters at the throat has a major effect on the wormholes’ gravitational dynamics and their ability to form traversable spacetime paths. We examine the influence of deformation factors on the horizon structure and find a strong relationship between these variables and the Schwarzschild-AdS horizon radius. The study also investigates whether various equations of state affect the stability of wormholes. We find that deformation parameters improve the wormhole throat’s stability for the barotropic EoS, with stable regions growing as the deformation parameter rises. Our research shows both stable and unstable areas in the context of a phantom-like variable equation of state, with the stability landscape expanding as the deformation parameter increases. Higher deformation parameter values enhance gravitational balance and stability, whereas increasing the variable constant $$n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> </mml:math> produces more oscillatory patterns in the effective potential, according to the Chaplygin variable EoS analysis, which reveals a complex stability landscape. We also study the massive and massless scalar field dynamics near the neck of the wormhole. We discover that for massless fields, the effective potential tends to zero as the shell radius rises, allowing traversable wormholes to emerge. In contrast, greater pressure values for massive scalar fields result in deeper potential wells, which strengthens the stability of the shell and lends more credence to the viability of traversable wormholes.