Abstract
In this study, we conduct an analysis of traversable wormhole solutions within the framework of linear gravity, ensuring that all energy conditions hold for the entire spacetime. The solutions presented in this paper are derived through a comprehensive analytical examination of the parameter space associated with the wormhole model. This involves considering the exponents governing the redshift and shape functions, as well as the radius of the wormhole throat (), the redshift function value at the throat (), and the model parameters (α and β). Moreover, we establish bounds on these free parameters, which guarantee the satisfaction of the energy conditions throughout spacetime and also provide two solutions. Furthermore, we use the Israel junction condition to observe the stability of a thin-shell around the wormhole. Finally, we calculate the null energy condition criteria as well as the potential for the thin-shell and how it varies with the chosen shape function.
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