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In this paper, we study the spherically symmetric Dirac star model in thepresence of a phantom field, obtaining a traversable wormhole solution innon-trivial topological spacetime. This solution exhibits asymmetry in both thefield configuration and the metric and possesses a finite ADM mass $M$ andNoether charge $Q$. Furthermore, we find that due to the presence of a wormholeat the center, this solution exhibits many differences from the Dirac starunder trivial spacetime. Notably, when the wormhole throat size is small, ournumerical calculations indicate the emergence of an extremely approximate blackhole solution on one side of the wormhole spacetime, a phenomenon unexplored.At this time, the Kretschmann scalar near the throat tends to infinity,indicating the wormhole becomes untraversable.

Emergency of black holes from wormholes