Traversable Wormhole Solutions admitting Karmarkar Condition in $f(R,T)$ Theory

Abstract: In this paper, we evaluate traversable wormhole solutions through Karmarkar condition in $f(R,T)$ theory, where $T$ is the trace of the energy-momentum tensor and $R$ represents the Ricci scalar. We develop a wormhole shape function for the static traversable wormhole geometry by using the embedding class-I technique. The resulting shape function is used to construct wormhole geometry that fulfills all the necessary conditions and joins the two asymptotically flat regions of the spacetime. We investigate the existence of viable traversable wormhole solutions for anisotropic matter configuration and examine the stable state of these solutions for different $f(R,T)$ gravity models. We analyze the graphical behavior of null energy bound to examine the presence of physically viable wormhole geometry. It is found that viable and stable traversable wormhole solutions exist in this modified theory of gravity.