We construct a model for the nucleation of a wormhole within a Lorentzian spacetime by employing techniques from topological surgery and Morse theory. In our framework, a 0-surgery process describes the neighborhood of the nucleation point inside a compact region of spacetime, yielding a singular Lorentzian cobordism that connects two spacelike regions with different topologies. To avoid the singularity at the critical point of the Morse function, we employ the Misner trick of taking a connected sum with a closed 4-manifold—namely, ${\mathbb{CP}}^2$—to obtain an everywhere nondegenerate Lorentzian metric. This connected sum replaces the naked singularity with a region containing closed timelike curves. The obtained spacetime is nonsingular but violates all the standard energy conditions. Our construction, thus, shows that a wormhole can be “created” without singularities in classical general relativity.

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• General relativity
• General relativity equations & solutions
• Singularities In general relativity
• Spacetime topology & causal structure