Wormhole Nucleation via Topological Surgery in Lorentzian Geometry

TL;DR

This paper models wormhole nucleation in Lorentzian spacetime using topological surgery, resulting in a nonsingular, energy-condition-violating spacetime with closed timelike curves.

Contribution

It introduces a novel topological surgery method to create nonsingular wormholes in classical general relativity.

Findings

Constructs a nonsingular Lorentzian spacetime with a wormhole.

Replaces singularities with regions containing closed timelike curves.

Demonstrates wormhole creation without energy condition violations at the cost of closed timelike curves.

Abstract

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.