Simple analytic model of wormhole formation

TL;DR

This paper presents a straightforward analytic model for wormhole formation by connecting Minkowski and Roberts spacetimes, showing that the resulting curvature singularity is weak and transient during the formation process.

Contribution

It introduces a simple explicit solution modeling wormhole formation through spacetime gluing, highlighting the transient nature of the singularity involved.

Findings

The model successfully describes wormhole formation with a weak, instantaneous singularity.

The spacetime is constructed by gluing Minkowski and Roberts solutions at null hypersurfaces.

The singularity disappears instantaneously and is weak along radial causal geodesics.

Abstract

An explicit and simple solution representing the wormhole formation is presented. The spacetime is constructed by gluing the Minkowski and Roberts spacetimes at null hypersurfaces in a regular manner. The parameters in the Roberts solution are required to give the negative kinetic term for the massless scalar field. Although a curvature singularity appears at the moment of the wormhole formation, it disappears instantaneously. This instantaneous singularity is weak in the senses of both Tipler and Kr\'{o}lak along radial causal geodesics.