Abstract
This paper aims to explore the viable and stable geometry of traversable wormholes in the framework of f(R,Lm) theory. For this purpose, we build a shape function using the Karmarkar condition that determines the geometry of the wormhole. The resulting shape function meets all the fundamental requirements and successfully establishes a connection between two asymptotically flat regions of the spacetime. We then formulate the field equations corresponding to two different models of this theory, representing static spherically symmetric anisotropic fluid distribution. We also check feasibility of the obtained wormhole solutions by graphically analyzing the behavior of null energy conditions. Finally, we examine the stability of these solutions through the speed of sound and adiabatic index criteria. We conclude that both our resulting models are well-agreed with the requirements needed for the existence of wormholes for chosen parametric values.
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