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Abstract This study explores the wormhole solutions utilizing the notion of conformal symmetry in the background of the gravity. The exact shape functions are calculated using the Gaussian and Lorentzian distributions as the noncommutative source of the energy density. All the energy conditions are checked for the two different shape functions. The presence of exotic matter is confirmed due to the violation of the null energy conditions. The physical aspects of the epicyclic frequencies of test particles are discussed in the spacetime geometry of the obtained wormholes in the current analysis and it is shown that how they depend on the spacetime parameters. The red‐blue shifts for the photons emitted by the orbiting test particles are also investigated and their dependence on the spacetime parameters is discussed. Further, the stability of the developed structure of the traversable wormholes is investigated by using the Tolman‐Oppenheimer‐Volkoff equation.
Mustafa et al. (Tue,) studied this question.
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